The soldier was killed by an improvised explosive device in Afghanistan's Nangarhar Province while carrying out operations against the militant group, according to a statement by the US military Tuesday.
The explosion killed three Afghan soldiers as well, Amaq said, Reuters reported.
Daesh has attracted hundreds, perhaps thousands, of fighters in Afghanistan and Pakistan to join its ranks, and holds some territory in Nangarhar. But it has not been able to expand its influence in Afghanistan beyond a few districts and the Taliban remain the dominant militant force there.