[Update 4:43 p.m. ET] The U.S. Department of Defense identified the two sailors. Coalition troops found the body of Petty Officer, 2nd Class Justin McNeley, 30, of Wheatridge, Colorado, while Petty Officer 3rd Class Jarod Newlove, 25, of Renton, Washington, is still missing.
[Original post 7:50 a.m. ET] The remains of an American sailor who went missing last week have been found in eastern Afghanistan, NATO's International Security Assistance Force said Tuesday.
"Afghan and coalition forces recovered the remains of a missing ISAF service member Sunday in eastern Afghanistan after an extensive search," the ISAF statement said. The search continues for the other service member, according to ISAF.
ISAF has not identified the missing service members or their nationalities, but the U.S. Navy confirmed Sunday that they are American sailors.
"The thoughts and prayers of our entire Navy go out to the missing sailors serving in Afghanistan and their families," said Adm. Gary Roughead, chief of U.S. naval operations, in the statement. "We have been closely following the situation from the outset. These sailors represent two of several thousand sailors serving on the ground in Afghanistan in support of U.S. Forces-Afghanistan and the International Security Assistance Force Afghanistan.
"Forces on the ground in Afghanistan are doing everything they can to locate and safely return our missing shipmates," Roughead said.
On Sunday, provincial government officials confirmed the death of one of the American sailors.
Den Mohammad Darwish, the spokesman for the governor of Logar province, said he learned from locals that the American was killed. He said the body was found in the Patanak Mountains of Charkh district. He also said the vehicle the men were driving was located Sunday.
A Taliban spokesman confirmed that the American died in a firefight and the other is being held by the group.
Taliban spokesman Zabiullah Mujahid said the two Americans were driving in a civilian vehicle in the village of Dasht, in Charkh district.
The Taliban wanted to take both men alive, but the firefight broke out, killing one of the Americans, Mujahid said. The other is alive and being held in a safe location, he said
There were no immediate demands from the Taliban for the return of the Americans because the group was still deliberating what its demands would be, Mujahid said.
A U.S. military official confirmed that a $20,000 reward was being offered for information leading to the return of the two sailors. Posters were being distributed in the region.
– CNN's Atia Abawi and Barbara Starr contributed to this report.