The International Court of Justice is hearing a suit that alleges 52 Mexican citizens on U.S. death row were denied a fair trial because they weren't told they had a right to help from the Mexican consulate.
Mexico asked the court on Monday to order the men's cases be returned to the moment of their arrest and started again.
But representing the United States, William Taft — great-grandson of President and Chief Justice William Howard Taft — said the request was "unprecedented" and the international court was "not a criminal appeal court."
The court already "traveled a considerable distance" in a previous rulings against the United States, Taft said. "The United States urges that it go no further."
The International Court of Justice, also known as the world court, is the U.N. judicial body for resolving disputes between countries.
At the center of Mexico's claim is the Vienna Convention, a 1963 treaty signed by both countries that says people traveling or living abroad have the right to contact their consulates when they are accused of a serious crime.
Mexico argued Monday that because consular help "could have, in capital proceedings, made the difference between life and death" for the men, the only fair way to repair the wrong was to start the legal process over.
But Taft argued Tuesday that in a similar case in 2001, the court had ruled that the remedy "must be left to the United States. Must be."
He said that otherwise, U.S. police and prosecutors in every jurisdiction would be "held hostage" while they coordinated their criminal investigations with foreign consulates.
In the 2001 case, the court found that the United States had failed to inform a German citizen of his right to consular assistance.
But Walter LaGrand had already been executed in Arizona, in defiance of an injunction by the international court.
Hearings in the Mexico case conclude Friday. No date has been set for a ruling.
The case drew international attention in February, when the court's 15-judge panel unanimously ordered the United States to delay the executions of three men until it could hear the case in full.
Mexicans Cesar Fierro, Roberto Ramos and Osbaldo Torres remain on U.S. death row, and none has had an execution date set.
In November, the U.S. Supreme Court declined to hear an appeal based on the Vienna Convention from Torres, who was convicted of killing two people during a burglary in Oklahoma City in 1993.
But in a dissenting opinion, Justice Stephen Breyer wrote that it was "manifestly unfair" for U.S. courts to ignore such appeals.
"It surely is reasonable to presume that most foreign nationals are unaware of the provisions of the Vienna Convention (as are, it seems, many local prosecutors)," Breyer wrote.
Fierro and Ramos are both on death row in Texas, Fierro for shooting a taxi driver to death, and Ramos for killing his wife and two children with a hammer.
The other 51 Mexicans named in the suit are imprisoned in California, Texas, Arizona, Arkansas, Florida, Nevada, Ohio, Oklahoma and Oregon.
In all, there are 120 foreign nationals from 29 countries on death row in various states, according to the Death Penalty Information Center.
Mexican President Vincente Fox canceled a visit with President Bush last year after the execution in Texas of a Mexican man who was not included in the petition.
By Toby Sterling