"A total of three US service members died today in the incident in Jordan," the official said in Washington.
"The service members were in vehicles approaching the gate of a Jordanian military training facility, where they came under small arms fire," the official added.
"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.
The army said an investigation was under way to determine the causes of the shooting.
An American defence official described the incident as "green on blue", a military term for when friendly forces attack US personnel.
The death of three American troops in Jordan could prove very embarrassing for Amman, a key recipient of US financial aid and member of the US-led coalition fighting the Islamic State group in neighbouring Syria and Iraq.
US forces have trained a small group of vetted Syrian rebels in Jordan, and American instructors have trained Iraqi and Palestinian security forces in Jordan as well over the past few years.
Today's incident comes almost a year after a Jordanian policeman shot dead two US instructors, a South African and two Jordanians at a police training centre east of Amman, before being gunned down.
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