A Jordanian military source said the shootout took place on Friday as the vehicle transporting the trainers failed to stop at the gate of the Prince Faisal airbase.
"There was an exchange of fire at the entrance to the base after an attempt by the trainers' vehicle to enter the gate without heeding orders of the guards to stop," the source said.
The incident also left another US trainer and a Jordanian army guard wounded.
"An investigation is now under way to know exactly what happened," the source added.
The US embassy in Jordan confirmed the shooting.
"We have reports of a security incident involving American personnel and we are in contact with Jordanian officials who are giving us all the support," the embassy said in a statement.
The incident comes about a year after a Jordanian police officer shot dead two US government contractors, a South African trainer and two Jordanians at a US-funded police training facility near Amman, the capital of Jordan, before being killed in a shootout.
A US official said at the time that the two Americans killed on November 9, 2015, were working with the US Department of State's International Narcotics and Law Enforcement Affairs Bureau and were responsible for training Palestinian forces.
Jordan is a key ally of the United States in the Middle East as well as an active part of the so-called US-led coalition against the Daesh Takfiri terror group. The US uses Jordanian airfields to station warplanes for its campaign in Syria.
The United States and its allies have been conducting airstrikes against purported positions of Daesh inside Syria without any authorization from Damascus or a UN mandate since September 2014.
Since the beginning of the crisis in Syria in 2011, hundreds of Jordanians have reportedly joined terrorist groups operating against the government of Syrian President Bashar al-Assad.
Jordan also hosts hundreds of American military personnel as part of a program to allegedly reinforce the kingdom’s defense.
The United States has also trained militants in Jordan for operations in Syria, Press TV reported.
219