US President Donald Trump says Iranian cultural sites are fair game for the US military, dismissing concerns within his own administration that doing so could constitute a war crime under international law.

He also warned Iraq he would levy punishing sanctions if it expelled American troops in retaliation for a US airstrike in Baghdad that killed a top Iranian official.

Mr Trump’s comments came amid escalating tensions in the Middle East following the assassination of General Qassem Soleimani, the head of Iran’s elite Quds force.

Iran has vowed to retaliate and Iraq’s parliament responded by voting on Sunday to oust US troops based in the country.

Mr Trump first raised the prospect of targeting Iranian cultural sites Saturday in a tweet. Speaking with reporters as he flew back to Washington from his holiday stay in Florida on Sunday he doubled down, despite international prohibitions.

“They’re allowed to kill our people. They’re allowed to torture and maim our people.

"They’re allowed to use roadside bombs and blow up our people. And we’re not allowed to touch their cultural sites? It doesn’t work that way,” Trump said.

The killing of General Soleimani sparked outrage in the Middle East, including in Iraq, where more than 5,000 American troops are still on the ground 17 years after the US invasion.

Gen Soleimani was killed 'to stop war, not start one', says Trump. Credit: AP

Iraq’s parliament voted on Sunday in favour of a non-binding resolution calling for the expulsion of the American forces.

Mr Trump said the US would not leave without being paid for its military investments in Iraq over the years — then said if the troops do have to withdraw, he would hit Baghdad with economic penalties.

“We will charge them sanctions like they’ve never seen before ever. It’ll make Iranian sanctions look somewhat tame,” he said. “If there’s any hostility, that they do anything we think is inappropriate, we are going to put sanctions on Iraq, very big sanctions on Iraq.”

He added: “We’re not leaving until they pay us back for it.”

The administration has scrambled to contend with the backlash to the killing of General Soleimani.

Though he was responsible for the deaths of hundreds of Americans, the American strike marked a stark escalation in tensions between Washington and Tehran.

Secretary of State Mike Pompeo said the US military may well strike more Iranian leaders if the Islamic Republic retaliates. He tip-toed around questions about Mr Trump’s threat to attack Iranian cultural sites, a military action that likely would be illegal under the laws of armed conflict and the UN charter.

Mr Pompeo said any US military strikes inside Iran would be legal.

“We’ll behave inside the system,” Mr Pompeo said. “We always have and we always will.”

Mr Trump’s warnings have alarmed some other world leaders - many of whom have been calling for calm.

British PM Boris Johnson returned from holiday and broke his silence on the rising tension in the Middle East.

The prime minister said he wouldn't "lament" the killing of Soleimani but called for a 'de-escalation' of the crisis.

Mourners surround a truck carrying flag draped coffins of General Qassem Soleimani and his comrades who were killed in last Friday’s US drone strike, in the southwestern Iranian city of Ahvaz on Sunday Credit: Mohammad Mohsenifar/Mehr News Agency/AP

In a joint statement on Monday, Mr Johnson and his French and German counterparts have called for all sides to work towards an urgent easing of tensions in the Persian Gulf.

The prime minister, Emmanuel Macron and Angela Merkel said that while they were concerned by the “negative” role Iran has played in the region – including through forces directed by Soleimani – there was now “an urgent need for de-escalation”.

Iranian state television reported the country would no longer abide by any limits of the 2015 nuclear deal it signed with the United States and other world powers.

Mr Trump withdrew the US from the deal in 2018 and stepped up economic sanctions on Tehran — actions that accelerated a cycle of hostilities leading to the last Friday’s assassination.

Mr Pompeo said the administration would have been “culpably negligent” in its duty to protect the United States if it had not killed him.

He did not provide evidence for his previous claims that General Soleimani was plotting imminent attacks on Americans. Instead of arguing an attack had been imminent, he said it was inevitable.

“We watched him continue to actively build out for what was going to be a significant attack – that’s what we believed – and we made the right decision,” he said.

“We continue to prepare for whatever it is the Iranian regime may put in front of us within the next 10 minutes, within the next 10 days, and within the next 10 weeks.”

Some Congressional Democrats were sceptical.

“I really worry that the actions the president took will get us into what he calls another endless war in the Middle East. He promised we wouldn’t have that,” said Chuck Schumer of New York, the Senate’s top Democrat.

Mr Schumer said Mr Trump lacked the authority to engage militarily with Iran and Congress needs a new war powers resolution “to be a check on this president.” To which Pompeo said: “We have all the authority we need to do what we’ve done to date.”

But Mr Trump made clear on Sunday he sees little reason to give Congress advanced warning if he orders the military to carry out further actions against Iran.

“These Media Posts will serve as notification to the United States Congress that should Iran strike any US person or target, the United States will quickly & fully strike back, & perhaps in a disproportionate manner,” he wrote on Twitter. “Such legal notice is not required, but is given nevertheless!”