Mr Trump, in a televised address from the White House, said no US or Iraqi lives were lost in the attacks and the bases suffered only minimal damage.

The Irbil and Al Asad bases were attacked early on Wednesday local time.

Iran said it acted in retaliation after the assassination of top Iranian General Qasem Soleimani last week.

The US drone strike targeting him and Iran-backed militia figures in the Iraqi capital Baghdad was a major escalation amid already deteriorating relations between Iran and the US.

Iran’s Supreme Leader Ali Khamenei described the missile attacks as a “slap in the face” for the US and called for an end to the American presence in the Middle East.

On Wednesday evening at least two rockets fell in Baghdad’s heavily fortified Green Zone, where the US embassy is located. There were no reports of any damage or casualties.

The US attack on Soleimani killed members of pro-Iranian Iraqi militias, who have also said they would seek revenge.