Kabul, Afghanistan (CNN) -- One of two American service members who were abducted in Afghanistan on Friday has been killed, provincial government officials said Sunday.
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 killed American died in a firefight and the other is being held by the group.
Another official, Samar Gul Rashid -- who is the governor of the Charkh district in Logar province -- also confirmed the killing, saying he learned about it through Afghan intelligence officials.
In releasing a statement Sunday, the Navy confirmed that the two missing service members are 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.
Rashid said the second sailor, who was also abducted, is wounded and still missing.
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.
Adm. Mike Mullen told reporters earlier Sunday that he could not give out any information. But he did call it an "unusual circumstance" to have two individuals leave the base and drive over an hour away in a non-military vehicle.
The two went missing after leaving their compound in the Afghan capital of Kabul, NATO said.
An Afghan intelligence source told CNN that the two were abducted in Logar province, south of Kabul.
The development comes as five U.S. soldiers were killed in bombings in southern Afghanistan on Saturday.
CNN's Atia Abawi and Barbara Starr contributed to this report.