The case involved Jose Medellin, who was denied the right to meet with a consular officer from Mexico after his arrest for murder.
The World Court in The Hague in 2004 ordered the United States to review the cases of Medellin and 50 other Mexican death row inmates because U.S. officials failed to tell them of their right under the Vienna Convention to talk to consular officers immediately after their arrests.
Bush in 2005 decided to comply with the World Court's ruling and he directed state courts to review the 51 cases to determine whether the violation of their rights caused the defendants any harm at trial or at sentencing.
Bush's action caused the Supreme Court to dismiss an earlier appeal by Medellin without deciding the merits of the dispute and to send the case back to the Texas courts.
After losing before the Texas Court of Criminal Appeals, Medellin's attorneys again appealed to the Supreme Court. They said the Texas court has put the United States in violation of its undisputed treaty obligations.
Bush administration attorneys supported Medellin's appeal. They said Bush acted within his authority and that the Texas court invalidated a presidential action "on a matter of international importance."
Medellin, a gang member, was sentenced to death in state court for the 1993 rape and murder of two teenage girls in Houston. The brutal killings stemmed from a gang initiation.
Lawyers for the state opposed the appeal. They said Bush exceeded his authority and that he cannot pre-empt Texas criminal law.
The Supreme Court will hear arguments and decide the case during its upcoming term that begins in October.