"A total of three US service members died today in the incident in Jordan ," the official said in Washington.
"Initial reports were that one was killed, two injured. The two injured service members were transported to a hospital in Amman, where they died."
"We are working with the Jordanian government to gather additional details about what happened."
It said that a Jordanian officer was also wounded.
"An exchange of fire occurred Friday morning at the gate of the Prince Feisal Air Base in Al-Jafr when a car carrying trainers attempted to enter the gate without heeding the guards' orders to stop," it said in a statement, quoting a military source.