WASHINGTON  In a death-penalty case that has become an international issue, the Supreme Court declared on Tuesday that President Bush had no power to tell the State of Texas to reopen the case of a Mexican who has been condemned for murder and rape.

By 6 to 3, the court ruled that the president went too far in 2005, when he decreed that the states had to abide by a 2004 decision by the World Court. That decision found that several dozen Mexican citizens who had been sentenced to death in the United States had not been given the assistance from Mexican diplomats that they were entitled to receive under an international treaty.

The center of the dispute is Jose E. Medellin, now 33, a onetime gang member in Houston who took part in the rape and slaying of two teenaged girls on June 24, 1993. The victims were abused for an hour, then killed to prevent them from identifying their tormentors. Mr. Medellin strangled one girl with her shoelaces, the trial revealed.

He was arrested five days later, and signed a confession after being given his Miranda rights. Crucially, however, the law enforcement authorities neglected to tell him of his right under the Vienna Convention to notify Mexican diplomats of his detention.