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President Donald Trump and his top officials mounted a full court press Tuesday defending the killing of Qassem Soleimani, the top Iranian commander blown up in a U.S. airstrike last week, amid continuing criticism over the move.

Trump said Soleimani, whom he called a "monster" responsible for recently killing an American and injuring several others, was planning a "very big attack and a very bad attack for us" and that the United States would be ready to retaliate if Iran sought revenge. But the president appeared to walk back a previous statement saying he would bomb cultural sites in Iran.

"We are, according to the various laws, supposed to be very careful with their cultural heritage. And you know what, if that's what the law is, I like to obey the law," Trump said. "But think of it, they kill our people, they blow up our people and we have to be very gentle with their cultural institutions. But I'm OK with it. It's OK with me.

"I will say this: If Iran does anything that they shouldn't be doing, they're going to be suffering the consequences and very strongly," he said.

Trump made his remarks before Iran fired more than a dozen ballistic missiles at two Iraqi air bases housing U.S. troops on Wednesday Iraq time.

Secretary of State Mike Pompeo, asked Tuesday about Trump's threat to attack Iranian heritage sites, said Tehran's actions had done more to harm the country's culture than anything the United States had done.

"Let me tell you who has done damage to the Persian culture. It's not the United States of America. It's the ayatollah," Pompeo referring to Iran's supreme leader, Ayatollah Ali Khamenei, said at a news press conference in response to a question from NBC News' chief foreign correspondent, Andrea Mitchell.

"If you want to look at who has denied religious freedom ... Persian culture is rich and steeped in history and intellect, and they've denied the capacity for that culture to continue," he said, adding: "The real risk to Persian culture does not come from the United States of America."

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Trump reiterated that the United States wasn't ready to leave Iraq despite a vote by the country's parliament to expel U.S. forces.

"We want to be able to let Iraq run its own affairs, and that's very important, so at some point we want to get out," Trump said. "But this isn't the right point."

Defense Secretary Mark Esper called on Iran to "de-escalate" to "prevent further bloodshed."

"The United States is not seeking a war with Iran, but we are prepared to finish one," he said at a press conference Tuesday. "We are seeking a diplomatic solution, but first it requires Iran to de-escalate."

Esper also sidestepped a question about whether he would resign if the president orders officials to attack Iranian cultural sites.

"I'm fully confident that the commander in chief would not give us an illegal order, and as I said, the United States military will, as it always has, obey the laws of armed conflict," he said.

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In remarks to reporters on Air Force One on Sunday night, Trump suggested that the United States could attack Iranian cultural sites if Iran retaliated for the killing of Soleimani, one of the country's top military and intelligence officials.

"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 president's comments came after he posted a vaguely worded tweet that said the United States would attack 52 Iranian sites following any retaliation from Tehran. International laws prohibit attacks on cultural sites.

In his own Twitter response Sunday, Iranian Foreign Minister Mohammad Javad Zarif called the suggestion that the United States would target cultural sites a "war crime."

At Monday's news conference, Pompeo said the administration would work within international law when responding to an attack from Iran.

"Every target that's being reviewed, every effort that is being made, will always be conducted inside the international laws of war," he said. "I have worked on this project, and I'm very confident of that."

Pompeo also reiterated his defense that classified U.S. intelligence showed that Soleimani had been involved in planning an imminent attack on Americans.

"It was the right decision," he said. "We got it right."

Pompeo also called Zarif "a propagandist of the first order" after Zarif was reported to have said Soleimani was traveling to Baghdad on a diplomatic mission with Iraqi officials.

"We know that wasn't true. We not only know the history, we know in that moment that was not true," Pompeo said. "It's not new. We have heard the same lies before. It's fundamentally false. He was not there on a diplomatic mission trying to resolve a problem."