The Taliban wants to trade the body of an American sailor killed during a firefight Friday for captured Taliban prisoners, according to an Afghan government official.

The announcement came as Washington confirmed that two men from the U.S. Navy went missing in the province of Logar, which is in the country's eastern section.

Officials said the pair disappeared after their armoured SUV drove into an area which is controlled by the Taliban.

Taliban spokesman Zabiullah Mujahid told The Associated Press by phone Sunday that a gunfight broke out in Logar after the U.S. vehicle entered the insurgent-controlled area.

He added that one of the men was killed during the gun battle. Both the deceased man and the other man were taken to a "safe area" and "are in the hands of the Taliban," said Mujahid.

However, Mujahid did not say that a prisoner exchange was being offered. In an earlier conversation on Sunday, Mujahid was not aware of the capture.

Nonetheless, an Afghan government official said that the message of the prisoner exchange was sent through intermediaries.

Abdul Wali, who is a provincial deputy head, said local officials responded to the Taliban's message by saying "Let's talk about the one that is still alive."

It isn't clear what the response has been.

A $20,000 reward is also being offered for the sailors' safe return. Hundreds of posters have been put up in the area since the pair went missing.

The posters state: "This American troop is missing. He was last seen in a white Land Cruiser vehicle. If you have any information about this solider, kindly contact the Logar Joint Co-ordination Center."

According to Logar province spokesman Din Mohammed Darwesh, the sailors had left their base without notifying Afghan officials. There also has been no clear explanation from NATO as to why the sailors were in Logar in the first place.

Local witnesses said that an SUV was spotted in the area on Friday night and the occupants later visited a bazaar in the Charkh district.

Taliban insurgents spotted the men at the bazaar and then kept an eye on them, said Charkh official Samer Gul.

"The Taliban saw them in the bazaar," he said. "They didn't touch them in the bazaar, but notified other Taliban that a four-wheel vehicle was coming their way."

But when a second Taliban group in a separate vehicle approached the U.S. SUV, gunfire was exchanged.

U.S Adm. Mike Mullen said that NATO was still piecing together what exactly occurred, adding that "from what I know right now, this is an unusual circumstance."

"There's a tremendous amount of effort going on to find them, to search, and beyond that I can't discuss any additional details at this time. It serves to remind of the challenges that we have and also the service and sacrifice that so many make, but that's really all I can talk about."