WASHINGTON — US President Donald Trump on Sunday vowed "major retaliation" if Iran tries to avenge the killing of its key military commander Qasem Soleimani and doubled down on a threat to bomb Iranian cultural sites.

"If they do anything there will be major retaliation," Trump told reporters.

Trump, speaking on Air Force One on his way back to Washington from a vacation in Florida, also said he would impose "very big sanctions" on Iraq if it follows through on a parliament vote calling for the expulsion of US troops based in the country.

The president's rhetoric added to already spiralling tensions in the Middle East following the killing by the United States of Soleimani – one of the most important figures in the Iranian government – in a drone strike near Baghdad's international airport.

Trump had already threatened widespread bombing of Iran if Tehran carries out its own threats to attack US troops and interests in the region.

In his latest comments, he dismissed strong criticism of his earlier warnings that targets could include unspecified cultural sites in Iran – a country with an ancient heritage.

"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 site? It doesn't work that way," he said.

Trump's reaction to the Iraqi parliament vote urging the departure of US troops also illustrated the widening fallout from the decision to kill Soleimani last week.

He said that Iraq, a US ally, would be treated like foe Iran, whose economy has been devastated by US-led sanctions, if the troops were made to exit on unfavourable terms.

"If they do ask us to leave – if we don't do it in a very friendly basis – we will charge them sanctions like they've never seen before," Trump said.

"It'll make Iranian sanctions look somewhat tame."

Trump said the US base in Iraq was "very extraordinarily expensive."

"We're not leaving unless they pay us back for it," he said. — AFP