The international military coalition says in a statement that it is investigating the cause of Monday's crash.
NATO says rescue forces came under fire from insurgents but had safely moved all crew and passengers to a nearby base by early morning.
Kunar provincial spokesman Safiullah Wasifullah Wasify says the helicopter went down before dawn in Kunar's remote mountainous Chapa Dara district. He says that his report showed it was shot down by a rocket.
Taliban spokesman Zabiullah Mujahid said that troops were dropping out of the helicopter for an assault on the militant group when they shot the helicopter down.