A senior Iraqi cleric has urged supporters not to attack the United States, shortly after Donald Trump said Iran appeared to be backing down from its bellicose threats.

"I call on the Iraqi factions to be deliberate, patient, and not to start military actions, and to shut down the extremist voices of some rogue elements until all political, parliamentary and international methods have been exhausted," said influential Iraqi Shi'ite cleric Moqtada al-Sadr.

It came after Donald Trump urged Britain and others to "recognise reality" and withdraw from the Iran nuclear deal in response to an Iranian missile strike on US forces in Iraq earlier on Wednesday.

The US president said Iran appeared to be backing down after it fired the 22 missiles, but announced fresh sanctions on Iran and he singled out the United Kingdom as one of the members of the ailing nuclear deal, urging Boris Johnson to follow America's lead and withdraw from the pact. Mr Trump pulled out of the nuclear deal in 2018.

"The very defective JCPOA expires shortly anyway and gives Iran a clear and quick path to nuclear breakout," he told a press conference at the White House.

"Iran must abandon its nuclear ambitions and end its support for terrorism...the time has come for the United Kingdom, Germany, France, Russia and China to recognise this reality."

He added: "They must now break away from the remnants of the Iran deal - or JCPOA - and we must all work together towards making a deal with Iran that makes the world a safer and more peaceful place."

It came as US officials speculated that Iran 'aimed to miss' when it fired missiles at US forces, it emerged there were no casualties in the rocket barrage.