There was no dispute that authorities in Oregon and Virginia violated the treaty, the Vienna Convention on Consular Relations, in the two cases that were before the court in a single extended argument.
Article 36 of the treaty, which the United States ratified in 1969, gives people who are arrested and detained in a foreign country a right known as consular notification, which dictates that they be informed that at their request their country's diplomats will be notified and made available to advise them.
Neither Moises Sanchez-Llamas, a Mexican who was convicted of attempted murder in Oregon for shooting a police officer, nor Mario A. Bustillo, a Honduran convicted of a gang-related murder in Springfield, Va., a Washington suburb, received the required notice at the time of their arrests.
The question was what remedy, if any, existed for the violation. Five lawyers debated the issue: one for each defendant, the solicitors general of Oregon and Virginia, and a deputy United States solicitor general.
The three government officials argued that the treaty governs relationships between nations, and that the remedy for a violation of consular notification was limited to a diplomatic protest or formal apology. The United States in fact issued a formal apology to Honduras in the case of Mr. Bustillo, who is serving a 30-year sentence for the 1997 killing.
The lawyers for the defendants argued that so limited a view ran counter to the undisputed principle that a treaty, once ratified, becomes part of a country's domestic law. Consequently, they argued, foreign defendants should have access to the same remedies that the legal system offers for government violations of rights protected by American law.
Accordingly, Mr. Sanchez-Llamas is arguing that incriminating statements he made to the police be suppressed because he had not received his consular notification at the time he made them. His lawyer's argument that such an exclusion should apply — similar to the rule that bars the introduction of illegally seized evidence — was rejected by the Oregon Supreme Court and did not make much headway with the justices on Wednesday.
After the lawyer, Peter Gartlan, acknowledged that the Vienna Convention says nothing about suppressing evidence, Chief Justice John G. Roberts Jr. asked, "So if the treaty doesn't say 'suppress,' what authority does a federal court have to tell a state court to suppress?"
The other defendant, Mr. Bustillo, is arguing that he is entitled to reversal of his conviction on the ground that Honduran officials, had they been notified of his arrest, would have helped identify another Honduran man who returned to Honduras after the murder and who, Mr. Bustillo asserts, was the real killer.
His lawyer, Mark T. Stancil, argued that because Virginia was not forced to reopen the case to permit the new evidence, the state was able to benefit from its violation of the Vienna Convention.
Here, too, the justices were skeptical. Several suggested that the fact that Mr. Bustillo had been provided with a lawyer was enough to insulate any Vienna Convention violation. The state, they said, had a right to expect that lawyers would inform their clients of their Vienna Convention rights.
"The lawyer should be taxed with knowing it because it's the law of the land," Justice David H. Souter said, referring to the treaty.
The International Court of Justice, often referred to as the World Court, takes the view that the convention confers individual rights. It ruled in 2004, in a case brought by Mexico, that the United States could not permit the execution of 51 Mexicans, on death row in various states, who had not received their consular notification.
After that ruling, and while a Supreme Court appeal brought by one of the Mexicans, José Ernesto Medellín, was pending, the Bush administration withdrew the United States from the provision of the treaty that gives the World Court jurisdiction over disputes of this kind. At the same time, the administration told state courts to abide by the decision. The Supreme Court dismissed the Medellín case last May without ruling on the enforceability of the Vienna Convention.
Deputy Solicitor General Gregory G. Garre was asked about the World Court's position by Justice Stephen G. Breyer, who referred to that court by its initials, I. C J.
Mr. Garre replied, "To be blunt, the I. C. J. decision is wrong." He said that while the World Court was entitled to "respectful consideration," its decision was "certainly not" binding on the United States.
Mr. Garre said that the State Department was making "extensive efforts" to make sure state and local governments were aware of the need to inform foreign defendants of the right to consular notification. The department has distributed 600,000 cards to police departments, he said, adding, "These efforts are working."
But it appeared that Vienna Convention issues would probably not disappear. Justice Anthony M. Kennedy asked Mary H. Williams, the Oregon solicitor general, why the police, who already give Miranda warnings, could not simply be told to ascertain the citizenship of people they take into custody so that the required notice could be given.
That was "not so easy," said Ms. Williams.
"I don't see why it's so complicated," Justice Kennedy said. He was joined by Justice Souter, who asked Ms. Williams, "You ask his name, why not his citizenship?"
Ms. Williams replied, "We're moving toward that goal."
Justice Souter was less than satisfied. "Why does it have to be a distant goal?" he asked.
The cases are Sanchez-Llamas v. Oregon, No. 04-10566, and Bustillo v. Johnson, No. 05-51.