US special forces in Jordan in 2013. Photograph: Maya Alleruzzo/AP

Two US military trainers have been killed and a third American has been wounded in an exchange of fire at a Jordanian air force base, the Jordanian army has said.

The army said the incident happened when a car carrying the Americans failed to stop at the gate of the airbase in al-Jafr, in the south of the country.

It said a Jordanian officer was also wounded, and an investigation was under way to determine the causes of the shooting.

The US embassy in Jordan acknowledged a “security incident involving US personnel”, but gave few other details.

“We are in contact with the appropriate Jordanian authorities, who have offered their full support. We will report more information when available and appropriate,” it said.

The deaths could prove very embarrassing for Amman, a key recipient of US financial assistance and a member of the US-led coalition fighting Islamic State 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 over the past few years.

Friday’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 himself being gunned down.

Washington said at the time that the two Americans killed were employees of the private firm DynCorp, contracted by the state department to train Palestinian forces. Two other Americans were wounded in that incident, which sparked concern in Washington and was condemned by the US embassy.

The centre where last year’s shooting took place was set up after the US-led invasion of Iraq in 2003. It has trained tens of thousands of Iraqi, Palestinian and Afghani police officers, and last year Jordan announced that former Libyan rebels would also be trained there.

A government source said military training was provided at al-Jafr airbase by instructors of various nationalities, including Americans, to participants from different countries.

Last year, the US announced its intention to increase overall US assistance to Jordan from $660m to $1bn (£800m) annually from 2015-17.