In a statement, it identified the dead soldiers as Staff Sergeants Matthew C. Lewellen, 27, of Lawrence, Kansas; Kevin J. McEnroe, 30, of Tucson, Arizona; and James F. Moriarty, 27, of Kerrville, Texas.
Details of the deadly incident - unusual given the close political and military ties between Washington and Amman - remain under investigation.
A Jordanian military source told Reuters the US trainers were fired on by Jordanian security forces when they failed to stop at the gate of Prince Faisal air base in the south of the country.
Other Jordanian sources, however, said they could not rule out political motives in the incident.