At issue is the case of William Osborne, who was convicted in a brutal attack on a prostitute in Alaska 16 years ago. He won a federal appeals court ruling granting him access to a blue condom that was used during the attack. Testing its contents would firmly establish his innocence or guilt, says Osborne, who has admitted his guilt in a bid for parole.

But several justices said something more should be required, including a sworn declaration of innocence that would hold out the prospect of additional punishment for lying under oath.

One condition, Justice David Souter said, is that an "individual claiming the right to test claims that he is actually innocent."

People who waived DNA testing at the time of their trial also might not be able to test it later, some justices suggested.

The Obama administration, backing Alaska prosecutors, urged the court to reject the ruling of the federal appeals court in San Francisco in favor of Osborne.

Deputy Solicitor General Neal Katyal said the decision by the 9th U.S. Circuit Court of Appeals was too broad and would erase the requirement in the federal DNA testing law that a person must assert his innocence under penalty of perjury before getting access to the evidence.

Osborne has never made that claim and in fact admitted his guilt as part of his parole proceedings, Katyal said.