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President Donald Trump dug in Sunday night on his threat to attack Iranian cultural sites if Tehran retaliates for the killing of Gen. Qassem Soleimani, one of Iran's top military and intelligence officials.

Speaking aboard Air Force One on his return to Washington on Sunday from a holiday at his Mar-a-Lago resort in Florida, Trump said: "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 was responding to backlash over the threat he made via Twitter on Saturday to attack 52 targets if Iran retaliates and his claim in a tweet that those targets would be "at a very high level & important to Iran & the Iranian culture," according to a pool report.

Asked about fears Iran might retaliate, the president told reporters: "If it happens, it happens. If they do anything, there will be major retaliation."

Trump told reporters the U.S. had surveillance on Soleimani going back 18 months. "He was leading his country down a very bad dangerous path," Trump said.

Iranian Foreign Minister Mohammad Javad Zarif called the suggestion that the U.S. military would target cultural sites a "war crime" in his own Twitter response.

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Protocol I of the Geneva Convention prohibits the targeting of "historic monuments, works of art or places of worship which constitute the cultural or spiritual heritage of peoples," while also prohibiting making such sites the "object of reprisals."

But Secretary of State Mike Pompeo batted down the idea that the U.S. would violate the law with any strikes. "The American people should know that we have prepared for this, that we are ready, that our responses are lawful, and that the president will take every action necessary to respond should Iran decide to escalate," Pompeo told Chuck Todd on "Meet the Press" on Sunday.

The president's rhetoric comes despite backlash over his threat to cultural sites, including from some in his own party. "We shouldn't be attacking cultural sites. And I don't see our military planners suggesting or identifying sites to hit," Rep. Will Hurd, R-Texas, said on MSNBC on Sunday night.

"And we should be focused on targeting the folks that are involved in conducting terrorism, the folks that are putting down their own people," Hurd added.

Speaker Nancy Pelosi, D-Calif., is expected to introduce a War Powers Resolution in the House this week to limit the president’s military actions regarding Iran.

Trump on Sunday night also sounded a note of defiance over the news that Iraq's Parliament voted to expel U.S. troops from the country. He said military personnel would not leave unless Iraq pays the U.S. back for an air base there.

"We have a very extraordinarily expensive air base that’s there. It cost billions of dollars to build. Long before my time," Trump said. "We’re not leaving unless they pay us back for it."

The president went on to say that if Iraq forces the U.S. military out, "we will charge them sanctions like they’ve never seen before ever. It'll make Iranian sanctions look somewhat tame."

"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," Trump said.

Iraq's prime minister has scheduled a meeting Monday with the American ambassador to discuss the U.S. role in Iraq, according to two officials familiar with the planning.

The officials say Iraqi Prime Minister Adil Abdul-Mahdi is expected to tell Ambassador Matthew Tueller that U.S. troops will have to leave the country, and he is expected to ask for a timeline.