Pentagon officials have confirmed that all 16 bodies have been recovered from the site where one of their Chinook helicopters crashed earlier this week.
The troops were flying to join an operation against militants
Lieutenant General James Conway gave no further details on how the Chinook came down, but the US has already conceded "hostile fire" may have been to blame.
The Taleban say they shot down the aircraft, which was carrying soldiers to the eastern province of Konar.
The US military had earlier said that 17 soldiers were on board.
The servicemen were on their way to join operations against militants when the Chinook came down.
US forces have been engaged in a number of combat missions in south-east Afghanistan against Taleban and al-Qaeda militants and their allies opposed to the Kabul government.
If the reports of hostile fire are confirmed, the Chinook would be the first US helicopter to be downed in such a way in Afghanistan since March 2002.
US troops reached the crash site in a remote mountain valley late on Wednesday night.
Bad weather had hampered the search, which has been further complicated by the high altitude of the crash site.
Officials say the rugged mountain terrain had made it difficult for the rescue team to reach the area.
Earlier, the governor of Konar province, Asadullah Waffa, told the BBC the helicopter had been brought down by a rocket.
He said the attack was the work of well-funded militants who had entered Afghanistan planning to spread chaos before September's parliamentary elections.
His security forces recently arrested two such militants posing as cameramen, he said.
A man claiming to be a spokesman for the Taleban told the BBC its supporters had shot the helicopter down.
He said he had video of the crash and its aftermath but our correspondent says there is still no sign of it.
A second man also claiming to speak for the Taleban phoned two international news agencies in Afghanistan with similar claims.
US military forces regularly come under attack in Konar province.
There has recently been an increase in fighting between US-led troops and militants.