The unusual request, from Louisiana and the Bush administration, was based on the failure of anyone involved in the case to take into account a federal law from 2006 that authorizes the death penalty for members of the military who are convicted of child rape.
The state argued that the case should be reopened because Justice Anthony Kennedy relied in part on what he called a "national consensus" against executing convicted rapists. The court split 5-4 in the June 25 ruling.
The justices, by a 7-2 vote, issued an amended opinion Wednesday that adds a footnote concerning military law, but otherwise leaves the essence of the decision untouched.
The provision of military law setting out punishments for rapists "does not draw into question our conclusions that there is a consensus against the death penalty for the crime in the civilian context and that the penalty here is unconstitutional," Kennedy wrote, joined by the four liberal justices who formed the majority in June.
Reopening the case would have taken five votes, including that of at least one justice who voted to ban the death penalty for rapists.
Justices Samuel Alito and Clarence Thomas voted to hear the case again.
Chief Justice John Roberts and Justice Antonin Scalia dissented from the original opinion, but voted against reopening the case.
The number of jurisdictions that allowed for capital punishment for rapists was irrelevant to the court's decision, Scalia said. Instead, the justices in the majority employed their independent judgment to say the Constitution forbids executions when the defendant does not kill the victim, he said.
"There is no reason to believe that absence of a national consensus would provoke second thoughts," Scalia said, noting his strong disagreement with the initial ruling.
Lawyers for Patrick Kennedy, whose death sentence was overturned by the court, said the justices got it right the first time. Kennedy's lawyers said military law has long authorized death as punishment for rapes of adults and children, but that the military hasn't sought to execute a rapist in more than 40 years.
The administration took no position when the case was argued, but backed Louisiana's call for a new hearing. The administration said in court papers that Kennedy's opinion "rests on an erroneous and materially incomplete assessment of the 'national consensus' concerning child rape."