Three US Army sergeants Kevin McEnroe, Matthew Lewellen and James Moriarty from the 5th Special Forces Group (Airborne) from Fort Campbell, Kentucky were killed in the shooting outside the base in southern Jordan.
Embassy spokesman Eric Barbee says US investigators are considering all possible motives and "have not yet ruled out terrorism as a potential motive."
After the shooting, Jordan's state media reported that the slain American trainers had sparked a firefight by disobeying direct orders from the Jordanians.