The US suffered its worst single loss of life in the nearly 10-year Afghan war when a helicopter carrying 31 special forces soldiers crashed on Friday night in the east of the country.
Both the Taliban, via a spokesman reached by telephone, and Afghan officials in Wardak province, to the west of Kabul, said insurgents had shot down the Chinook helicoter with a rocket.
Nato would only confirm that "there was enemy activity in the area" and that the US-led alliance was still trying to work out what had happened. US air force captain Justin Brockhoff, a Nato spokesman, said: "We are in the process of accessing the facts."
A western official said 37 people were on board, all of whom were killed. The Afghan president, Hamid Karzai, said the helicopter was carrying 31 US special forces and seven members of the Afghan national army.
It is very unusual for Nato deaths from a single incident to reach double figures. The previous most deadly day for foreign troops was in June 2005 when 16 US soldiers were killed when a Taliban rocket hit a Chinook in the eastern province of Kunar.
The crash happened at 3am when the helicopter was hovering over the town of Tangi Joi Zareen, in the district of Saidabad, according to a spokesman for the provincial governor.
A Taliban spokesman, Zabiullah Mujahid, said Nato attacked a house in the district where insurgent fighters were gathering. He said eight insurgents died in the fighting.
Special forces from many nations, including the UK, conduct up to half a dozen such operations every night, usually targeting mid-level insurgent commanders whose whereabouts are pinpointed by high-tech intelligence gathering teams.
The downing of a helicopter, quite apart from the massive loss of life, will alarm war planners who rely heavily on Nato's air superiority in the fight against the Taliban. They will want to discover whether the aircraft was downed by a lucky shot from a rocket-propelled grenade, a highly inaccurate weapon, or by something more sophisticated.
The Soviet occupation of Afghanistan in the 1980s was greatly hindered by portable Stinger missile systems provided by the US and the far less effective Blowpipe weapons provided by the UK. Nato forces have intercepted so-called Manpads, or man-portable air defence systems, illegally smuggled from Iran and there have been recorded incidents when they have been used.
Classified military reports released by WikiLeaks last year showed that the US military covered up a reported surface-to-air missile strike that downed a Chinook helicopter over Helmand, killing seven soldiers.