This file photo shows debris after an airstrike in Syria.

The US has carried out air strikes against a pro-Iran militant group in Iraq, killing 19 fighters, two days after a rocket attack that killed an American civilian contractor.

The Pentagon said on Sunday it targeted weapons caches or command and control facilities linked to Kata'ib Hezbollah (KH) in Western Iraq, as well as Eastern Syria, in response to a barrage of 30 or more rockets fired on Friday.

US secretary of State Mike Pompeo speaks at news conference. File photo

Secretary of State Mike Pompeo said "we will not stand for the Islamic Republic of Iran to take actions that put American men and women in jeopardy".

Four US service members and Iraqi security forces were also wounded in Friday's attack at the K1 Iraqi military base in Kirkuk, an oil-rich region north of Baghdad.

US Defence Secretary Mark Esper said on Sunday the air strikes were successful, and he did not rule out further action to "deter further bad behavior from militia groups or from Iran".

Esper also said that he and Pompeo had travelled to Florida, where President Donald Trump has been spending the Christmas holidays, to brief him on the latest Middle East events.

US Defence Secretary Mark Esper said on Sunday the air strikes were successful. File photo

"KH has a strong linkage with Iran's Quds Force and has repeatedly received lethal aid and other support from Iran that it has used to attack" coalition forces, the Pentagon said earlier, referring to the external arm of Iran's Revolutionary Guards.

Nineteen fighters were killed by the US strikes in western Iraq, while several were wounded, according to an official from the Tehran-backed Hashed Al Shaabi paramilitary force.

A few hours later, four rockets exploded near a base housing US troops close to Iraq's capital without wounding anyone, an Iraqi security official told AFP.

The military spokesman for Iraq's outgoing prime minister Abel Abdel Mahdi decried "a violation of Iraqi sovereignty".

Another powerful pro-Iran faction, Assaib Ahl al-Haq — whose leaders were recently hit with US sanctions — called for Americans to withdraw from Iraq.

"The American military presence has become a burden for the Iraqi state and a source of threat against our forces," it said in a statement.