"We condemn this attack on Iraqi military bases hosting Coalition - including British - forces," said Foreign Secretary Dominic Raab.

"We are concerned by reports of casualties and use of ballistic missiles."

Iran fired missiles overnight at Iraqi bases housing the US and British military, officials in Washington and Tehran said.

It was the first act of the Islamic republic's promised revenge for the US killing of top Iranian general Qasem Soleimani last week.

Launched from Iranian territory and by Iranian forces not a proxy, the attack marked a new turn in the intensifying confrontation between the United States and Iran.

The Pentagon said it was still "working on initial battle damage assessments" after more than a dozen ballistic missiles were launched, with no immediate reports on casualties.

The Iraqi military said it sustained no casualties in 22 missile strikes on bases housing US troops.

Raab urged Iran to show restraint going forward.

"We urge Iran not to repeat these reckless and dangerous attacks, and instead to pursue urgent de-escalation," he added.

"A war in the Middle East would only benefit Daesh and other terrorist groups," Raab said, referring to the Islamic State group.