It says the drone was on a routine mission in international airspace when two Russian jets tried to intercept it.
The US European Command said Tuesday's crash was the result of an "unprofessional act by the Russians".
Russia said the drone crashed after a "sharp manoeuvre", and denied that the two aircraft made direct contact.
The Russian defence ministry also said the MQ-9 Reaper drone was flying with its transponders turned off. Transponders are communications devices that allow the aircraft to be tracked.
