Afghan President Hamid Karzai said 31 US special forces and seven Afghan soldiers were killed in a helicopter crash in eastern Wardak province.
It's the highest number of casualties recorded in a single incident in Afghanistan.
Mr Karzai said in a statement that he has sent condolences to President Barack Obama for the victims of the overnight crash.
The Taliban have claimed responsibility, saying their fighters downed the helicopter in a battle with Nato troops.
"A Nato helicopter crashed last night in Wardak province," Mr Karzai said in the statement, adding that 31 American special operations troops were killed.
"President Karzai expressed his deep condolences because of this incident and expressed his sympathy to Barack Obama."
Nato confirmed the overnight crash and said the alliance was conducting a recovery operation at the site and investigating the cause of the crash, but did not release details or a casualty figure. The coalition said there "was enemy activity in the area".
"We are aware of an incident involving a helicopter in eastern Afghanistan," said US Air Force Captain Justin Brockhoff, a Nato spokesman. "We are in the process of accessing the facts."
A spokesman for Wardak province, Shahidullah Shahid, said the helicopter crashed in the Sayd Abad district of Wardak province. The volatile region borders the province of Kabul where the Afghan capital is located and is known for its strong Taliban presence.
Taliban spokesman Zabiullah Mujahid claimed the downed aircraft was a US military helicopter and that the Taliban fighters had brought it down with a rocket attack.