[337]*337Chief Justice Roberts
delivered the opinion of the Court.
Article 36 of the Vienna Convention on Consular Relations (Vienna Convention or Convention), Apr. 24, 1963, [1970] 21 U. S. T. 77, 100-101, T. I. A. S. No. 6820, addresses communication between an individual and his consular officers when the individual is detained by authorities in a foreign country. These consolidated cases concern the availability of judicial relief for violations of Article 36. We are confronted with three questions. First, does Article 36 create rights that defendants may invoke against the detaining authorities in a criminal trial or in a postconviction proceeding? Second, does a violation of Article 36 require suppression of a defendant’s statements to police? Third, may a State, in a postconviction proceeding, treat a defendant’s Article 36 claim as defaulted because he failed to raise the claim at trial? We conclude, even assuming the Convention creates judicially enforceable rights, that suppression is not an appropriate remedy for a violation of Article 36, and that a State may apply its regular rules of procedural default to Article 36 claims. We therefore affirm the decisions below.
I
A
The Vienna Convention was drafted in 1963 with the purpose, evident in its preamble, of “contributing] to the development of friendly relations among nations, irrespective of their differing constitutional and social systems.” 21 U. S. T., at 79. The Convention consists of 79 articles regulating various aspects of consular activities. At present, 170 [338]*338countries are party to the Convention. The United States, upon the advice and consent of the Senate, ratified the Convention in 1969. Id., at 77.
Article 36 of the Convention concerns consular officers’ access to their nationals detained by authorities in a foreign country. The article provides that “if he so requests, the competent authorities of the receiving State shall, without delay, inform the consular post of the sending State if, within its consular district, a national of that State is arrested or committed to prison or to custody pending trial or is detained in any other manner.” Art. 36(l)(b), id., at 101.1 In other words, when a national of one country is detained by [339]*339authorities in another, the authorities must notify the consular officers of the detainee’s home country if the detainee so requests. Article 36(l)(b) further states that “[t]he said authorities shall inform the person concerned [L e., the detainee] without delay of his rights under this sub-paragraph.” Ibid. The Convention also provides guidance regarding how these requirements, and the other requirements of Article 36, are to be implemented:
“The rights referred to in paragraph 1 of this Article shall be exercised in conformity with the laws and regulations of the receiving State, subject to the proviso, however, that the said laws and regulations must enable full effect to be given to the purposes for which the rights accorded under this Article are intended.” Art. 36(2), ibid.
Along with the Vienna Convention, the United States ratified the Optional Protocol Concerning the Compulsory Settlement of Disputes (Optional Protocol or Protocol), Apr. 24, 1963, [1970] 21 U. S. T. 325, T. I. A. S. No. 6820. The Optional Protocol provides that “[disputes arising out of the interpretation or application of the Convention shall lie within the compulsory jurisdiction of the International Court of Justice [(ICJ)],” and allows parties to the Protocol to bring such disputes before the ICJ. Id., at 326. The United States gave notice of its withdrawal from the Optional Protocol on March 7, 2005. Letter from Condoleezza Rice, Secretary of State, to Kofi A. Annan, Secretary-General of the United Nations.
B
Petitioner Moisés Sanchez-Llamas is a Mexican national. In December 1999, he was involved in an exchange of gunfire with police in which one officer suffered a gunshot wound in the leg. Police arrested Sanchez-Llamas and gave him warnings under Miranda v. Arizona, 384 U. S. 436 (1966), in [340]*340both English and Spanish. At no time, however, did they inform him that he could ask to have the Mexican Consulate notified of his detention.
Shortly after the arrest and Miranda warnings, police interrogated Sanchez-Llamas with the assistance of an interpreter. In the course of the interrogation, Sanchez-Llamas made several incriminating statements regarding the shootout with police. He was charged with attempted aggravated murder, attempted murder, and several other offenses. Before trial, Sanchez-Llamas moved to suppress the statements he made to police. He argued that suppression was warranted because the statements were made involuntarily and because the authorities had failed to comply with Article 36 of the Vienna Convention. The trial court denied the motion. The case proceeded to trial, and Sanchez-Llamas was convicted and sentenced to 2OV2 years in prison.
He appealed, again arguing that the Vienna Convention violation required suppression of his statements. The Oregon Court of Appeals affirmed. Judgt. order reported at 191 Ore. App. 399, 84 P. 3d 1133 (2004). The Oregon Supreme Court also affirmed, concluding that Article 36 “does not create rights to consular access or notification that are enforceable by detained individuals in a judicial proceeding.” 338 Ore. 267, 276, 108 P. 3d 573, 578 (2005) (en banc). We granted certiorari. 546 U. S. 1001 (2005).
C
Petitioner Mario Bustillo, a Honduran national, was with several other men at a restaurant in Springfield, Virginia, on the night of December 10, 1997. That evening, outside the restaurant, James Merry was struck in the head with a baseball bat as he stood smoking a cigarette. He died several days later. Several witnesses at the scene identified Bustillo as the assailant. Police arrested Bustillo the morning after the attack and eventually charged him with mur[341]*341der. Authorities never informed him that he could request to have the Honduran Consulate notified of his detention.
At trial, the defense pursued a theory that another man, known as “Sirena,” was responsible for the attack. Two defense witnesses testified that Bustillo was not the killer. One of the witnesses specifically identified the attacker as Sirena. In addition, a third defense witness stated that she had seen Sirena on a flight to Honduras the day after the victim died. In its closing argument before the jury, the prosecution dismissed the defense theory about Sirena. See App. in No. 05-51, p. 21 (“This whole Sirena thing, I don’t want to dwell on it too much. It’s very convenient that Mr. Sirena apparently isn’t available”). A jury convicted Bustillo of first-degree murder, and he was sentenced to 30 years in prison. His conviction and sentence were affirmed on appeal.
After his conviction became final, Bustillo filed a petition for a writ of habeas corpus in state court. There, for the first time, he argued that authorities had violated his right to consular notification under Article 36 of the Vienna Convention. He claimed that if he had been advised of his right to confer with the Honduran Consulate, he “would have done so without delay.” App. in No. 05-51, at 60. Moreover, the Honduran Consulate executed an affidavit stating that “it would have endeavoured to help Mr. Bustillo in his defense” had it learned of his detention prior to trial. Id., at 74. Bustillo insisted that the consulate could have helped him locate Sirena prior to trial. His habeas petition also argued, as part of a claim of ineffective assistance of counsel, that his attorney should have advised him of his right to notify the Honduran Consulate of his arrest and detention.2
[342]*342The state habeas court dismissed Bustillo’s Vienna Convention claim as “procedurally barred” because he had failed to raise the issue at trial or on appeal. App. to Pet. for Cert, in No. 05-51, p. 43a. The court also denied Bustillo’s claim of ineffective assistance of counsel, ruling that his belated claim that counsel should have informed him of his Vienna Convention rights was barred by the applicable statute of limitations and also meritless under Strickland v. Washington, 466 U. S. 668 (1984). App. in No. 05-51, at 132. In an order refusing Bustillo’s petition for appeal, the Supreme Court of Virginia found “no reversible error” in the habeas court’s dismissal of the Vienna Convention claim. App. to Pet. for Cert, in No. 05-51, at la. We granted certiorari to consider the Vienna Convention issue. 546 U. S. 1001 (2005).
II
We granted certiorari as to three questions presented in these cases: (1) whether Article 36 of the Vienna Convention grants rights that may be invoked by individuals in a judicial proceeding; (2) whether suppression of evidence is a proper remedy for a violation of Article 36; and (3) whether an Article 36 claim may be deemed forfeited under state procedural rules because a defendant failed to raise the claim at trial.
As a predicate to their claims for relief, Sanchez-Llamas and Bustillo each argue that Article 36 grants them an individually enforceable right to request that their consular officers be notified of their detention, and an accompanying [343]*343right to be informed by authorities of the availability of consular notification. Respondents and the United States, as amicus curiae, strongly dispute this contention. They argue that “there is a presumption that a treaty will be enforced through political and diplomatic channels, rather than through the courts.” Brief for United States 11; ibid, (quoting Head Money Cases, 112 U. S. 580, 598 (1884) (a treaty “ ‘is primarily a compact between independent nations,’ ” and “ ‘depends for the enforcement of its provisions on the interest and the honor of the governments which are parties to it’”)). Because we conclude that Sanchez-Llamas and Bustillo are not in any event entitled to relief on their claims, we find it unnecessary to resolve the question whether the Vienna Convention grants individuals enforceable rights. Therefore, for purposes of addressing petitioners’ claims, we assume, without deciding, that Article 36 does grant Bustillo and Sanchez-Llamas such rights.
Sanchez-Llamas argues that the trial court was required to suppress his statements to police because authorities never told him of his rights under Article 36. He refrains, however, from arguing that the Vienna Convention itself mandates suppression. We think this a wise concession. The Convention does not prescribe specific remedies for violations of Article 36. Rather, it expressly leaves the implementation of Article 36 to domestic law: Rights under Article 36 are to “be exercised in conformity with the laws and regulations of the receiving State.” Art. 36(2), 21 U. S. T., at 101. As far as the text of the Convention is concerned, the question of the availability of the exclusionary rule for Article 36 violations is a matter of domestic law.
It would be startling if the Convention were read to require suppression. The exclusionary rule as we know it is an entirely American legal creation. See Bivens v. Six Unknown Fed. Narcotics Agents, 403 U. S. 388, 415 (1971) [344]*344(Burger, C. J., dissenting) (the exclusionary rule “is unique to American jurisprudence”). More than 40 years after the drafting of the Convention, the automatic exclusionary rule applied in our courts is still “universally rejected” by other countries. Bradley, Mapp Goes Abroad, 52 Case W. Res. L. Rev. 375, 399-400 (2001); see also Zicherman v. Korean Air Lines Co., 516 U. S. 217, 226 (1996) (postratification understanding “traditionally considered” as an aid to treaty interpretation). It is implausible that other signatories to the Convention thought it to require a remedy that nearly all refuse to recognize as a matter of domestic law. There is no reason to suppose that Sanchez-Llamas would be afforded the relief he seeks here in any of the other 169 countries party to the Vienna Convention.3
[345]*345For good reason then, Sanchez-Llamas argues only that suppression is required because it is the appropriate remedy for an Article 36 violation under United States law, and urges us to require suppression for Article 36 violations as a matter of our “authority to develop remedies for the enforcement of federal law in state-court criminal proceedings.” Reply Brief for Petitioner in No. 04-10566, p. 11.
For their part, the State of Oregon and the United States, as amicus curiae, contend that we lack any such authority over state-court proceedings. They argue that our cases suppressing evidence obtained in violation of federal statutes are grounded in our supervisory authority over the federal courts—an authority that does not extend to state-court proceedings. Brief for Respondent in No. 04-10566, pp. 42-43; Brief for United States 32-34; see McNabb v. United States, 318 U. S. 332, 341 (1943) (suppressing evidence for violation of federal statute requiring persons arrested without a warrant to be promptly presented to a judicial officer); Mallory v. United States, 354 U. S. 449 (1957) (suppressing evidence for violation of similar requirement of Fed. Rule Crim. Proc. 5(a)); Miller v. United States, 357 U. S. 301 (1958) (suppressing evidence obtained incident to an arrest that violated 18 U. S. C. § 3109). Unless required to do so by the Convention itself, they argue, we cannot direct Oregon courts to exclude Sanchez-Llamas’ statements from his criminal trial.
To the extent Sanchez-Llamas argues that we should invoke our supervisory authority, the law is clear: “It is beyond dispute that we do not hold a supervisory power over the courts of the several States.” Dickerson v. United States, 530 U. S. 428, 438 (2000); see also Smith v. Phillips, 455 U. S. 209, 221 (1982) (“Federal courts hold no supervisory authority over state judicial proceedings and may intervene only to correct wrongs of constitutional dimension”). The cases on [346]*346which Sanchez-Llamas principally relies are inapplicable in light of the limited reach of our supervisory powers. Mallory and McNabb plainly rest on our supervisory authority. Mallory, supra, at 453; McNabb, supra, at 340. And while Miller is not clear about its authority for requiring suppression, we have understood it to have a similar basis. See Ker v. California, 374 U. S. 23, 31 (1963).
We also agree with the State of Oregon and the United States that our authority to create a judicial remedy applicable in state court must lie, if anywhere, in the treaty itself. Under the Constitution, the President has the power, “by and with the Advice and Consent of the Senate, to make Treaties.” Art. II, § 2, cl. 2. The United States ratified the Convention with the expectation that it would be interpreted according to its terms. See 1 Restatement (Third) of Foreign Relations Law of the United States § 325(1) (1986) (“An international agreement is to be interpreted in good faith in accordance with the ordinary meaning to be given to its terms in their context and in the light of its object and purpose”). If we were to require suppression for Article 36 violations without some authority in the Convention, we would in effect be supplementing those terms by enlarging the obligations of the United States under the Convention. This is entirely inconsistent with the judicial function. Cf. The Amiable Isabella, 6 Wheat. 1, 71 (1821) (Story, J.) (“[T]o alter, amend, or add to any treaty, by inserting any clause, whether small or great, important or trivial, would be on our part an usurpation of power, and not an exercise of judicial functions. It would be to make, and not to construe a treaty”).
Of course, it is well established that a self-executing treaty binds the States pursuant to the Supremacy Clause, and that the States therefore must recognize the force of the treaty in the course of adjudicating the rights of litigants. See, e. g., Hauenstein v. Lynham, 100 U. S. 483 (1880). And where a treaty provides for a particular judicial remedy, [347]*347there is no issue of intruding on the constitutional prerogatives of the States or the other federal branches. Courts must apply the remedy as a requirement of federal law. Cf. 18 U. S. C. § 2515; United States v. Giordano, 416 U. S. 505, 524-525 (1974). But where a treaty does not provide a particular remedy, either expressly or implicitly, it is not for the federal courts to impose one on the States through lawmaking of their own.
Sanchez-Llamas argues that the language of the Convention implicitly requires a judicial remedy because it states that the laws and regulations governing the exercise of Article 36 rights “must enable full effect to be given to the purposes for which the rights ... are intended,” Art. 36(2), 21 U. S. T., at 101 (emphasis added). In his view, although “full effect” may not automatically require an exclusionary rule, it does require an appropriate judicial remedy of some kind. There is reason to doubt this interpretation. In particular, there is little indication that other parties to the Convention have interpreted Article 36 to require a judicial remedy in the context of criminal prosecutions. See Department of State Answers to Questions Posed by the First Circuit in United States v. Nai Fook Li, No. 97-2034 etc., p. A-9 (Oct. 15, 1999) (“We are unaware of any country party to the [Vienna Convention] that provides remedies for violations of consular notification through its domestic criminal justice system”).
Nevertheless, even if Sanchez-Llamas is correct that Article 36 implicitly requires a judicial remedy, the Convention equally states that Article 36 rights “shall be exercised in conformity with the laws and regulations of the receiving State.” Art. 36(2), 21 U. S. T., at 101. Under our domestic law, the exclusionary rule is not a remedy we apply lightly. “[0]ur cases have repeatedly emphasized that the rule’s ‘costly toll’ upon truth-seeking and law enforcement objectives presents a high obstacle for those urging application of the rule.” Pennsylvania Bd. of Probation and Parole v. [348]*348Scott, 524 U. S. 357, 364-365 (1998). Because the rule’s social costs are considerable, suppression is warranted only where the rule’s “ ‘remedial objectives are thought most efficaciously served.’” United States v. Leon, 468 U. S. 897, 908 (1984) (quoting United States v. Calandra, 414 U. S. 338, 348 (1974)).
We have applied the exclusionary rule primarily to deter constitutional violations. In particular, we have ruled that the Constitution requires the exclusion of evidence obtained by certain violations of the Fourth Amendment, see Taylor v. Alabama, 457 U. S. 687, 694 (1982) (arrests in violation of the Fourth Amendment); Mapp v. Ohio, 367 U. S. 643, 655-657 (1961) (unconstitutional searches and seizures), and confessions exacted by police in violation of the right against compelled self-incrimination or due process, see Dickerson, 530 U. S., at 435 (failure to give Miranda warnings); Payne v. Arkansas, 356 U. S. 560, 568 (1958) (involuntary confessions).
The few cases in which we have suppressed evidence for statutory violations do not help Sanchez-Llamas. In those cases, the excluded evidence arose directly out of statutory violations that implicated important Fourth and Fifth Amendment interests. McNdbb, for example, involved the suppression of incriminating statements obtained during a prolonged detention of the defendants, in violation of a statute requiring persons arrested without a warrant to be promptly presented to a judicial officer. We noted that the statutory right was intended to “avoid all the evil implications of secret interrogation of persons accused of crime,” 318 U. S., at 344, and later stated that McNabb was “responsive to the same considerations of Fifth Amendment policy that . . . face[d] us ... as to the States” in Miranda, 384 U. S., at 463. Similarly, in Miller, we required suppression of evidence that was the product of a search incident to an unlawful arrest. 357 U. S., at 305; see California v. Hodari D, 499 U. S. 621, 624 (1991) (“We have long understood that [349]*349the Fourth Amendment’s protection against 'unreasonable . . . seizures’ includes seizure of the person”).
The violation of the right to consular notification, in contrast, is at best remotely connected to the gathering of evidence. Article 36 has nothing whatsoever to do with searches or interrogations. Indeed, Article 36 does not guarantee defendants any assistance at all. The provision secures only a right of foreign nationals to have their consulate informed of their arrest or detention—not to have their consulate intervene, or to have law enforcement authorities cease their investigation pending any such notice or intervention. In most circumstances, there is likely to be little connection between an Article 36 violation and evidence or statements obtained by police.
Moreover, the reasons we often require suppression for Fourth and Fifth Amendment violations are entirely absent from the consular notification context. We require exclusion of coerced confessions both because we disapprove of such coercion and because such confessions tend to be unreliable. Watkins v. Sowders, 449 U. S. 341, 347 (1981). We exclude the fruits of unreasonable searches on the theory that without a strong deterrent, the constraints of the Fourth Amendment might be too easily disregarded by law enforcement. Elkins v. United States, 364 U. S. 206, 217 (1960). The situation here is quite different. The failure to inform a defendant of his Article 36 rights is unlikely, with any frequency, to produce unreliable confessions. And unlike the search-and-seizure context—where the need to obtain valuable evidence may tempt authorities to transgress Fourth Amendment limitations—police win little, if any, practical advantage from violating Article 36. Suppression would be a vastly disproportionate remedy for an Article 36 violation.
Sanchez-Llamas counters that the failure to inform defendants of their right to consular notification gives them [350]*350“a misleadingly incomplete picture of [their] legal options,” Brief for Petitioner in No. 04-10566, p. 42, and that suppression will give authorities an incentive to abide by Article 36.
Leaving aside the suggestion that it is the role of police generally to advise defendants of their legal options, we think other constitutional and statutory requirements effectively protect the interests served, in Sanchez-Llamas’ view, by Article 36. A foreign national detained on suspicion of crime, like anyone else in our country, enjoys under our system the protections of the Due Process Clause. Among other things, he is entitled to an attorney, and is protected against compelled self-incrimination. See Wong Wing v. United States, 163 U. S. 228, 238 (1896) (“[A]ll persons within the territory of the United States are entitled to the protection guaranteed by” the Fifth and Sixth Amendments). Article 36 adds little to these “legal options,” and we think it unnecessary to apply the exclusionary rule where other constitutional and statutory protections—many of them already enforced by the exclusionary rule—safeguard the same interests Sanchez-Llamas claims are advanced by Article 36.
Finally, suppression is not the only means of vindicating Vienna Convention rights. A defendant can raise an Article 36 claim as part of a broader challenge to the voluntariness of his statements to police. If he raises an Article 36 violation at trial, a court can make appropriate accommodations to ensure that the defendant secures, to the extent possible, the benefits of consular assistance. Of course, diplomatic avenues—the primary means of enforcing the Convention— also remain open.
In sum, neither the Vienna Convention itself nor our precedents applying the exclusionary rule support suppression of Sanchez-Llamas’ statements to police.
The Virginia courts denied petitioner Bustillo’s Article 36 claim on the ground that he failed to raise it at trial or on direct appeal. The general rule in federal habeas cases is [351]*351that a defendant who fails to raise a claim on direct appeal is barred from raising the claim on collateral review. See Massaro v. United States, 538 U. S. 500, 504 (2003); Bousley v. United States, 523 U. S. 614, 621 (1998). There is an exception if a defendant can demonstrate both “cause” for not raising the claim at trial, and “prejudice” from not having done so. Massaro, supra, at 504. Like many States, Virginia applies a similar rule in state postconviction proceedings, and did so here to bar Bustillo’s Vienna Convention claim. Normally, in our review of state-court judgments, such rules constitute an adequate and independent state-law ground preventing us from reviewing the federal claim. Coleman v. Thompson, 501 U. S. 722, 729 (1991). Bustillo contends, however, that state procedural default rules cannot apply to Article 36 claims. He argues that the Convention requires that Article 36 rights be given “‘full effect’” and that Virginia’s procedural default rules “prevented any effect (much less ‘full effect’) from being given to” those rights. Brief for Petitioner in No. 05-51, p. 35 (emphasis deleted).
This is not the first time we have been asked to set aside procedural default rules for a Vienna Convention claim. Respondent Johnson and the United States persuasively argue that this question is controlled by our decision in Breard v. Greene, 523 U. S. 371 (1998) (per curiam). In Breard, the petitioner failed to raise an Article 36 claim in state court— at trial or on collateral review—and then sought to have the claim heard in a subsequent federal habeas proceeding. Id., at 375. He argued that “the Convention is the ‘supreme law of the land’ and thus trumps the procedural default doctrine.” Ibid. We rejected this argument as “plainly incorrect,” for two reasons. Ibid. First, we observed, “it has been recognized in international law that, absent a clear and express statement to the contrary, the procedural rules of the forum State govern the implementation of the treaty in that State.” Ibid. Furthermore, we reasoned that while treaty protections such as Article 36 may constitute supreme federal law, this is “no less true of provisions of the Constitu[352]*352tion itself, to which rules of procedural default apply.” Id., at 376. In light of Breard’s holding, Bustillo faces an uphill task in arguing that the Convention requires States to set aside their procedural default rules for Article 36 claims.
Bustillo offers two reasons why Breará does not control his case. He first argues that Breard’s holding concerning procedural default was “unnecessary to the result,” Brief for Petitioner in No. 05-51, at 45, because the petitioner there could not demonstrate prejudice from the default and because, in any event, a subsequent federal statute—the Anti-terrorism and Effective Death Penalty Act of 1996,110 Stat. 1214—superseded any right the petitioner had under the Vienna Convention to have his claim heard on collateral review. We find Bustillo’s contention unpersuasive. Our resolution of the procedural default question in Breará was the principal reason for the denial of the petitioner’s claim, and the discussion of the issue occupied the bulk of our reasoning. See 523 U. S., at 375-377. It is no answer to argue, as Bustillo does, that the holding in Breará was “unnecessary” simply because the petitioner in that case had several ways to lose. See Richmond Screw Anchor Co. v. United States, 275 U. S. 331, 340 (1928).
Bustillo’s second reason is less easily dismissed. He argues that since Breará, the ICJ has interpreted the Vienna Convention to preclude the application of procedural default rules to Article 36 claims. The LaGrand Case (F. R. G. v. U. S.), 2001 I. C. J. 466 (Judgment of June 27) (LaGrand), and the Case Concerning Avena and other Mexican Nationals (Mex. v. U. S.), 2004 I. C. J. 12 (Judgment of Mar. 31) (Avena), were brought before the ICJ by the governments of Germany and Mexico, respectively, on behalf of several of their nationals facing death sentences in the United States. The foreign governments claimed that their nationals had not been informed of their right to consular notification. They further argued that application of the procedural default rule to their nationals’ Vienna Convention claims failed [353]*353to give “full effect” to the purposes of the Convention, as required by Article 36. The ICJ agreed, explaining that the defendants had procedurally defaulted their claims “because of the failure of the American authorities to comply with their obligation under Article 36.” LaGrand, supra, at 497, ¶ 91; see also Avena, supra, at 57, ¶ 113. Application of the procedural default rule in such circumstances, the ICJ reasoned, “prevented [courts] from attaching any legal significance” to the fact that the violation of Article 36 kept the foreign governments from assisting in their nationals’ defense. LaGrand, supra, at 497, ¶ 91; see also Avena, supra, at 57, ¶ 113.
Bustillo argues that LaGrand and Avena warrant revisiting the procedural default holding of Breard. In a similar vein, several amici contend that “the United States is obligated to comply with the Convention, as interpreted by the ICJ.” Brief for ICJ Experts 11 (emphasis added). We disagree. Although the ICJ’s interpretation deserves “respectful consideration,” Breard, supra, at 375, we conclude that it does not compel us to reconsider our understanding of the Convention in Breard.4
Under our Constitution, “[t]he judicial Power of the United States” is “vested in one supreme Court, and in such inferior Courts as the Congress may from time to time ordain and establish.” Art. Ill, § 1. That “judicial Power ... extend[s] to . . . Treaties.” Id., § 2. And, as Chief Justice Marshall famously explained, that judicial power includes the duty “to say what the law is.” Marbury v. Madison, 1 Cranch 137, 177 (1803). If treaties are to be given effect as federal law [354]*354under our legal system, determining their meaning as a matter of federal law “is emphatically the province and duty of the judicial department,” headed by the “one supreme Court” established by the Constitution. Ibid.; see also Williams v. Taylor, 529 U. S. 362, 378-379 (2000) (opinion of Stevens, J.) (“At the core of [the judicial] power is the federal courts’ independent responsibility—independent from its coequal branches in the Federal Government, and independent from the separate authority of the several States— to interpret federal law”). It is against this background that the United States ratified, and the Senate gave its advice and consent to, the various agreements that govern referral of Vienna Convention disputes to the ICJ.
Nothing in the structure or purpose of the ICJ suggests that its interpretations were intended to be conclusive on our courts.5 The ICJ’s decisions have “no binding force except between the parties and in respect of that particular case,” Statute of the International Court of Justice, Art. 59, 59 Stat. 1062, T. S. No. 993 (1945) (emphasis added). Any interpretation of law the ICJ renders in the course of resolving particu[355]*355lar disputes is thus not binding precedent even as to the ICJ itself; there is accordingly little reason to think that such interpretations were intended to be controlling on our courts. The ICJ’s principal purpose is to arbitrate particular disputes between national governments. Art. 1, id., at 1055 (ICJ is “the principal judicial organ of the United Nations”); see also Art. 34, id., at 1059 (“Only states [i e., countries] may be parties in cases before the Court”). While each member of the United Nations has agreed to comply with decisions of the ICJ “in any case to which it is a party,” United Nations Charter, Art. 94(1), 59 Stat. 1051, T. S. No. 993 (1945), the Charter’s procedure for noncompliance— referral to the Security Council by the aggrieved state— contemplates quintessential^ international remedies, Art. 94(2), ibid.
In addition, “[w]hile courts interpret treaties for themselves, the meaning given them by the departments of government particularly charged with their negotiation and enforcement is given great weight.” Kolovrat v. Oregon, 366 U. S. 187, 194 (1961). Although the United States has agreed to “discharge its international obligations” in having state courts give effect to the decision in Avena, it has not taken the view that the ICJ’s interpretation of Article 36 is binding on our courts. President Bush, Memorandum for the Attorney General (Feb. 28, 2005), App. to Brief for United States as Amicus Curiae in Medellin v. Dretke, O. T. 2004, No. 04-5928, p. 9a. Moreover, shortly after Avena, the United States withdrew from the Optional Protocol concerning Vienna Convention disputes. Whatever the effect of Avena and LaGrand before this withdrawal, it is doubtful that our courts should give decisive weight to the interpretation of a tribunal whose jurisdiction in this area is no longer recognized by the United States.
LaGrand and Avena are therefore entitled only to the “respectful consideration” due an interpretation of an international agreement by an international court. Breard, 523 [356]*356U. S., at 375. Even according such consideration, the ICJ’s interpretation cannot overcome the plain import of Article 36. As we explained in Breará, the procedural rules of domestic law generally govern the implementation of an international treaty. Ibid. In addition, Article 36 makes clear that the rights it provides “shall be exercised in conformity with the laws and regulations of the receiving State” provided that “full effect... be given to the purposes for which the rights accorded under this Article are intended.” Art. 36(2), 21 U. S. T., at 101. In the United States, this means that the rule of procedural default—which applies even to claimed violations of our Constitution, see Engle v. Isaac, 456 U. S. 107, 129 (1982)—applies also to Vienna Convention claims. Bustillo points to nothing in the drafting history of Article 36 or in the contemporary practice of other signatories that undermines this conclusion.
The IC J concluded that where a defendant was not notified of his rights under Article 36, application of the procedural default rule failed to give “full effect” to the purposes of Article 36 because it prevented courts from attaching “legal significance” to the Article 36 violation. LaGrand, 2001 I. C. J., at 497-498, ¶¶ 90-91. This reasoning overlooks the importance of procedural default rules in an adversary system, which relies chiefly on the parties to raise significant issues and present them to the courts in the appropriate manner at the appropriate time for adjudication. See Castro v. United States, 540 U. S. 375, 386 (2003) (Scalia, J., concurring in part and concurring in judgment) (“Our adversary system is designed around the premise that the parties know what is best for them, and are responsible for advancing the facts and arguments entitling them to relief”). Procedural default rules are designed to encourage parties to raise their claims promptly and to vindicate “the law’s important interest in the finality of judgments.” Massaro, 538 U. S., at 504. The consequence of failing to raise a claim for adjudication at the proper time is generally forfeiture of that [357]*357claim. As a result, rules such as procedural default routinely deny “legal significance”—in the Avena and LaGrand sense—to otherwise viable legal claims.
Procedural default rules generally take on greater importance in an adversary system such as ours than in the sort of magistrate-directed, inquisitorial legal system characteristic of many of the other countries that are signatories to the Vienna Convention. “What makes a system adversarial rather than inquisitorial is . . . the presence of a judge who does not (as an inquisitor does) conduct the factual and legal investigation himself, but instead decides on the basis of facts and arguments pro and con adduced by the parties.” McNeil v. Wisconsin, 501 U. S. 171, 181, n. 2 (1991). In an inquisitorial system, the failure to raise a legal error can in part be attributed to the magistrate, and thus to the state itself. In our system, however, the responsibility for failing to raise an issue generally rests with the parties themselves.
The ICJ’s interpretation of Article 36 is inconsistent with the basic framework of an adversary system. Under the ICJ’s reading of “full effect,” Article 36 claims could trump not only procedural default rules, but any number of other rules requiring parties to present their legal claims at the appropriate time for adjudication. If the state’s failure to inform the defendant of his Article 36 rights generally excuses the defendant’s failure to comply with relevant procedural rules, then presumably rules such as statutes of limitations and prohibitions against filing successive habeas petitions must also yield in the face of Article 36 claims. This sweeps too broadly, for it reads the “full effect” proviso in a way that leaves little room for Article 36’s clear instruction that Article 36 rights “shall be exercised in conformity with the laws and regulations of the receiving State.” Art. 36(2), 21 U. S. T., at 101.6
[358]*358Much as Sanchez-Llamas cannot show that suppression is an appropriate remedy for Article 36 violations under domestic law principles, so too Bustillo cannot show that normally applicable procedural default rules should be suspended in light of the type of right he claims. In this regard, a comparison of Article 36 and a suspect’s rights under Miranda disposes of Bustillo’s claim. Bustillo contends that applying procedural default rules to Article 36 rights denies such rights “full effect” because the violation itself—-1 e., the failure to inform defendants of their right to [359]*359consular notification—prevents them from becoming aware of their Article 36 rights and asserting them at trial. Of course, precisely the same thing is true of rights under Miranda. Police are required to advise suspects that they have a right to remain silent and a right to an attorney. See Miranda, 384 U. S., at 479; see also Dickerson, 530 U. S., at 435. If police do not give such warnings, and counsel fails to object, it is equally true that a suspect may not be “aware he even had such rights until well after his trial had concluded.” Brief for Petitioner in No. 05-51, at 35. Nevertheless, it is well established that where a defendant fails to raise a Miranda claim at trial, procedural default rules may bar him from raising the claim in a subsequent postconviction proceeding. Wainwright v. Sykes, 433 U. S. 72, 87 (1977).
Bustillo responds that an Article 36 claim more closely resembles a claim, under Brady v. Maryland, 373 U. S. 83 (1963), that the prosecution failed to disclose exculpatory evidence—a type of claim that often can be asserted for the first time only in postconviction proceedings. See United States v. Dominguez Benitez, 542 U. S. 74, 83, n. 9 (2004). The analogy is inapt. In the case of a Brady claim, it is impossible for the defendant to know as a factual matter that a violation has occurred before the exculpatory evidence is disclosed. By contrast, a defendant is well aware of the fact that he was not informed of his Article 36 rights, even if the legal significance of that fact eludes him.
Finally, relying on Massaro v. United States, 538 U. S. 500 (2003), Bustillo argues that Article 36 claims “are most appropriately raised post-trial or on collateral review.” Brief for Petitioner in No. 05-51, at 39. Massaro held that claims of ineffective assistance of counsel may be raised for the first time in a proceeding under 28 U. S. C. § 2255. That decision, however, involved the question of the proper forum for federal habeas claims. Bustillo, by contrast, asks us to require the States to hear Vienna Convention claims raised for the [360]*360first time in state postconviction proceedings. Given that the Convention itself imposes no such requirement, we do not perceive any grounds for us to revise state procedural rules in this fashion. See Dickerson, supra, at 438.
We therefore conclude, as we did in Breará, that claims under Article 36 of the Vienna Convention may be subjected to the same procedural default rules that apply generally to other federal-law claims.
* * *
Although these cases involve the delicate question of the application of an international treaty, the issues in many ways turn on established principles of domestic law. Our holding in no way disparages the importance of the Vienna Convention. The relief petitioners request is, by any measure, extraordinary. Sanchez-Llamas seeks a suppression remedy for an asserted right with little if any connection to the gathering of evidence; Bustillo requests an exception to procedural rules that is accorded to almost no other right, including many of our most fundamental constitutional protections. It is no slight to the Convention to deny petitioners’ claims under the same principles we would apply to an Act of Congress, or to the Constitution itself.
The judgments of the Supreme Court of Oregon and the Supreme Court of Virginia are affirmed.
It is so ordered.