The purpose of the stay, granted less than five hours before the scheduled execution, was to permit lawyers for the condemned man, Robin Lovitt, to file a full-scale Supreme Court appeal.
On Monday, the first day of its new term, the court rejected that appeal without comment.
The stay of execution will now automatically dissolve, leaving a grant of clemency by Virginia's governor, Mark Warner, the only way for Mr. Lovitt, 41, to avoid execution.
The court's action, in which Chief Justice John G. Roberts Jr. did not participate, runs counter to the impression created by several recent death penalty rulings that the Supreme Court is becoming more receptive to arguments raised on behalf of death row inmates.
Mr. Lovitt's appeal, filed by Kenneth W. Starr, the former solicitor general and independent counsel, contained 10 references to the most recent such ruling, Rompilla v. Beard, which the court issued in June.
In that case, the justices overturned a death sentence after concluding that the defendant's lawyer, in failing to search his background for facts that might persuade a jury to spare his life, had fallen below minimum constitutional standards for legal representation.
One argument in the case on Monday, Lovitt v. True, No. 05-5044, was that Mr. Lovitt's original defense lawyer had failed to present evidence of childhood abuse at the hands of a stepfather who gave the boy alcohol and narcotics before he was 10.
"By now, there can be no question," Mr. Starr asserted in Mr. Lovitt's Supreme Court brief. "Any competent counsel must conduct a thorough investigation of the defendant's background because the jury cannot reliably impose the death sentence without considering the petitioner's individual life history."
The brief added, "But that is not the law of the land as applied in the Fourth Circuit."
In April, the United States Court of Appeals for the Fourth Circuit in Richmond rejected Mr. Lovitt's petition for a writ of habeas corpus.
The other principal argument in the case concerned the destruction of evidence by a Virginia court clerk, after Mr. Lovitt's conviction had become final in state court but before he had filed a federal court petition.
The evidence was a pair of scissors that had been used in the fatal stabbing of the manager of a pool hall in Arlington, Va., during a robbery there.
The prosecution's theory was that Mr. Lovitt had used the scissors to pry open the cash register drawer and to stab the manager, Clayton Dicks, who caught him in the act. Mr. Lovitt's fingerprints were not on the scissors. DNA testing at the time showed the blood on the scissors to be that of the victim. The testing was inconclusive for the DNA of anyone else.
Mr. Lovitt's lawyers wanted a new, more modern test that they said would exclude him, and the appeal argued that discarding the scissors had resulted in "profound unfairness."
The brief said: "The commonwealth's wanton conduct has forever deprived Lovitt of a right, safeguarded under Virginia law, to test DNA evidence that had the potential to establish that he was wrongfully convicted."
Ordinarily, courts require a showing of bad faith before hearing an appeal based on loss of evidence by the officials responsible for maintaining it. There was no such showing in this case.
Just as the Supreme Court did not explain, on July 11, its reasons for granting a stay of execution, the court gave no reason on Monday for rejecting the appeal.
For the new term, the court has accepted five cases that deal with death penalty issues. One, House v. Bell, No. 04-8990, presents the question of what standard a death row inmate must meet for a federal court to hear a claim of innocence based on new DNA evidence. That case will be argued in January.
The Lovitt appeal was one of hundreds of cases the court turned down on Monday as it began the new term. Because Chief Justice Roberts had not yet been confirmed when the justices held their conference on these cases a week ago, he was listed as not having participated in any of the actions.