Two days after the US Navy sailors went missing in Logar province, just south of Kabul, NATO's International Security Assistance Force (ISAF) said it had no fresh information on their whereabouts.
After denying for 24 hours that they were involved, a Taliban spokesman Sunday claimed the insurgents had ambushed the pair, killing one and taking the other captive.
"One of the two was killed in the exchange of fire and we arrested the second alive," said Zabihullah Mujahid, speaking by telephone from an undisclosed location.
"We have taken both the body and the captured soldier with us and they have been carried to a safe location. We claim responsibility for it now," he told Awaz Apni.
The men went missing around 8:00pm (1530 GMT) on Friday in an area of Logar known to be dominated by Taliban-linked insurgents who have recently stepped up attacks on NATO-led troops, ISAF and local officials have said.
An ISAF official confirmed the pair as US Navy sailors but it was unclear where they were based, though they had set out from a camp in Kabul before they went missing.
"They didn't arrive where they had been expected so we don't know what happened to them between leaving the camp and then being reported missing," the official said, speaking on condition of anonymity.
"It is all speculation," he said.
US media reports suggested the two may have left their base without permission.
The Taliban warned earlier this year they would target foreign military and government installations and staff, as well as Afghans working for them or for the Kabul government.
A spokesman for Logar's provincial governor said the two "went to opposition territory".
"One of them has been killed and the other has been detained by the opposition," Din Mohammad Darwaish told Awaz Apni, referring to the Taliban.
The Awaz Apni quoted Darwaish as saying the pair had been warned not to venture into what was known Taliban territory, and had found themselves in a gun battle with insurgents, after which they were captured.
At least two Logar radio station broadcast descriptions of the men and offered rewards of ten thousand dollars for the safe return of each of them.
Posters with their photographs had a hotline to call with information but did not give their names.
The manhunt involved helicopters and vehicles and appeared to be targeting a large number of compounds suspected of harbouring Taliban fighters or bomb-makers.
ISAF said Sunday two suspected insurgents had been detained in Logar on Saturday night in "offensive clearing operations".
As the search for the missing men expanded, Washington's top-ranking military officer, Admiral Mike Mullen, visited Kabul for meetings with senior US officials including Ambassador Karl Eikenberry and General David Petraeus, commander of the 143,000 US and NATO troops fighting the Taliban.
"There is a tremendous amount of effort going on" to find the missing pair, Mullen told a press conference.
There has been rising violence in the east, where insurgents have staged a growing number of attacks in recent weeks, apparently in response to the arrival of American reinforcements, a senior officer said.
"We've seen an uptick in the number of IEDs (improvised explosive devices), the number of complex attacks, the number of small arms attacks," Major General John Campbell told reporters Sunday at a base in Bagram.
Kidnappings of foreign soldiers are rare in Afghanistan, where a nine-year insurgency has been escalating, particularly in the southern provinces of Helmand and Kandahar.
A 24-year-old US soldier, Bowe Bergdahl, who disappeared on June 30, 2009, is believed to have been the first American soldier snatched by militants in Afghanistan.
The Taliban have posted at least two videos on the Internet showing Bergdahl calling for his own release and for foreign troops to leave Afghanistan.
