ASHINGTON, March 28 - At first glance, the Bush administration's decision to comply with an international tribunal's order for new hearings for 51 Mexican nationals on death row might have appeared to resolve, or at least simplify, a pending Supreme Court case.

After all, new hearings are what the Mexicans are seeking in an appeal brought by one of them, a Texas death row inmate named Jose Ernesto Medellin. The Mexicans, inmates on the death rows of Texas and four other states, are arguing that their rights were violated when they were tried and convicted without the notice to their government that an international treaty requires.

But in arguments on Monday, it was apparent that the administration's new position has complicated rather than simplified the case, which now appears far from resolution. It also seemed that any resolution, at least for this phase of the case, was not to come from the justices, who appeared to be looking for ways to remove the appeal from their docket without deciding it.

The legal question the Supreme Court had originally agreed to decide was whether a federal appeals court had properly refused to consider Mr. Medellin's effort to invoke the Vienna Convention on Consular Relations to challenge his 1994 murder conviction and death sentence.

In refusing last year to accept Mr. Medellin's petition for a writ of habeas corpus, the United States Court of Appeals for the Fifth Circuit, in New Orleans, had relied on a 1998 Supreme Court precedent in a similar case, involving a Paraguayan national, to conclude that any rights under the Vienna Convention gave way to procedural barriers that Congress has established to limit state prison inmates' access to federal courts.

But between the Supreme Court's 1998 ruling and the Fifth Circuit's ruling last May, the legal landscape for inmates in Mr. Medellin's position changed. In March 2004, the International Court of Justice in the Hague, also known as the World Court, ruled in a lawsuit brought by Mexico against the United States that the Vienna Convention gave to 51 Mexicans who had not been informed at the time of their arrests that they could seek assistance from Mexican consular officials the right to "review and reconsideration" of their convictions and sentences.

Although the World Court's judgment ordered the United States to provide an "effective review" of each case, the Fifth Circuit concluded that the decision did not help Mr. Medellin. The Vienna Convention dealt with relations between governments and did not create an "individually enforceable right" on the part of criminal defendants, the appeals court held. It also said that Mr. Medellin's failure to raise the Vienna Convention issue at his trial meant that the ordinary rules of "procedural default" barred him from receiving any benefit from the World Court's ruling.

The Fifth Circuit's ruling was correct, the Bush administration informed the Supreme Court when it filed its brief earlier this month in the case, Medellin v. Dretke, No. 04-5928. But the brief added an unexpected wrinkle: an announcement that President Bush would comply with the World Court's decision, as an exercise of his "constitutionally based foreign affairs power," by directing the state courts to give the new hearings that the ruling required.

In arguments on Monday, Donald F. Donovan, representing Mr. Medellin, said the Supreme Court should retain jurisdiction over the case but should not decide it at this point, instead allowing the Texas courts to proceed.

"The president is giving effect to commitments made by the United States," and the court should defer to the administration's decision, Mr. Donovan said.

But some justices appeared to find that option unattractive. "Granting a stay could be seen as validating the position of the government without ever having written an opinion on it," Chief Justice William H. Rehnquist told Mr. Donovan. Based on the justices' responses, a more likely path would be to simply dismiss the case, which would have the same effect as if the court had never agreed to decide it in the first place.

R. Ted Cruz, the Texas solicitor general, urged the justices to decide the case by affirming the ruling of the Fifth Circuit and to leave other questions, including the individual rights of the defendant to assert claims under the treaty, to the Texas courts.

"This court should not, need not, address the many interesting questions of international law swirling around this case," Mr. Cruz said.

"They really are interesting," Justice Antonin Scalia agreed.

"They will launch a million law review articles," Mr. Cruz said.

Mr. Cruz resisted providing a direct answer to Justice David H. Souter's question on whether the Texas courts would accept the president's determination that they should provide a new review to a case they had already rejected.

"There are significant constitutional problems with a unilateral executive determination displacing state criminal law," Mr. Cruz said.

Michael R. Dreeben, a deputy United States solicitor general, said the Supreme Court would not need to resolve the "very sensitive and delicate questions" in the case if the Texas courts would accept the president's position and handle the case themselves. He said the president had decided that enforcing the World Court's judgment was "warranted as a matter of U.S. foreign policy" and that there would be "extraordinarily broad and detrimental foreign policy consequences" if the Mexican defendants did not get their hearings in state court.

Chief Justice Rehnquist was on the bench on Monday despite a problem with his tracheotomy tube that sent him to the hospital over the weekend. The court's public information office said that the chief justice had developed an unspecified problem and was taken in an ambulance to the Virginia Hospital Center, near his home in suburban Virginia, where he was treated on an outpatient basis. The chief justice, who is being treated for thyroid cancer and must speak through his tube, sounded huskier on Monday than he had last week, but appeared in good spirits.