An Aljazeera correspondent in Afghanistan said Muhamad Hanif, a spokesman for the Taliban, claimed that his movement had brought down the US Chinook.
The US-led forces said the 10 multinational force soldiers on board were all killed, but denied that the Chinook, which crashed near the Pakistan border, had been brought down by the Taliban.
"We have no indication that that happened," said a spokeswoman responding to Hanif's claim.
"The crash occurred in a very mountainous terrain and the landing zone was very difficult. It was a mountain-top landing zone.
"There were various weather factors that could have come into play ... There were high winds. We are investigating any possible causes for the accident but there were no enemy actions detected at the scene."
Hanif claimed that his movement has acquired advanced weaponry capable of destroying US helicopters.
The Taliban shot down another US Chinook helicopter in Kunar in June last year, killing all 16 soldiers on board. It was brought down by a rocket-propelled grenade, the US military said.
The aircraft that came down on Friday was taking part in an anti-Taliban offensive, Operation Mountain Lion, which was launched in Kunar last month.
Mountain Lion involves 2,500 Afghan and US-led troops backed by a range of US and British aircraft.
While those forces battle the Taliban and other fighters in eastern and southern Afghanistan, a separate Nato-led force of peacekeepers is deployed in the west and north, and in the capital, Kabul.