The Taliban had previously said they had killed one of the two men in a firefight and captured the other when they drove into a Taliban-held area.
"No one really seems to know and the military certainly aren't saying why [the soldiers] headed south into Logar province," Al Jazeera's James Bays, reporting from Kabul, said.
"What's also not clear is whether Nato recovered the remains after some sort of deal with the Taliban."
The Taliban has previously said that the captured soldier was in a "safe place" where he would not be found, but Nato said it would continue the hunt for the missing man.
Hundreds of fliers, with reprinted photos of the two missing sailors, have been distributed throughout Logar province where Nato troops were stopping vehicles, searching them and those inside.
The fliers said a $20,000 reward was being offered for information leading to the soldiers' location.
Jim Kerr, a Colorado legislator, named the dead sailor as Justin McNeley, his wife's 30-year-old nephew.
Kerr told The Denver Post that McNeley, a non-commissioned officer and father of two sons, was due to return to the US in August.
Another US soldier is also being held by the Taliban. Bowe Bergdahl disappeared June 30, 2009, in Paktika province, near Logar.
His fate and whereabouts remain unclear, although he appeared in a video released by the Taliban in April.