The region is where American troops are supporting Afghan security forces in a campaign against the Islamic State group's affiliate in Afghanistan.
The statement says two soldiers received minor injuries during the hard landing early today in the Achin district of eastern Nangarhar province.
It says the crew was rescued and that the aircraft was being recovered.
The Taliban in a statement claimed they opened fire on the helicopter, killing everyone on board. The insurgents routinely exaggerate their gains and casualties they inflict in battle.