Defense Secretary Mark Esper said on Monday that the military will not target cultural sites in Iran, which President Donald Trump has repeatedly threatened to do.

Esper acknowledged that attacking cultural sites with no military value would constitute a war crime, even though Trump insisted that it was appropriate for the U.S. to do so.

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“We will follow the laws of armed conflict,” Esper told reporters at a Monday press briefing, according to The New York Times .

Asked if that meant the U.S. would not hit cultural sites because it is a war crime, Esper agreed: “That’s the laws of armed conflict.”

The comments contradicted the president’s repeated threats. Trump on Thursday threatened to attack Iranian cultural sites if Iran retaliated after the assassination of top military commander Qassem Soleimani.

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“If Iran strikes any Americans, or American assets, we have targeted 52 Iranian sites (representing the 52 American hostages taken by Iran many years ago), some at a very high level & very important to Iran & the Iranian culture, and those targets, and Iran itself, WILL BE HIT VERY FAST AND VERY HARD,” Trump tweeted .

The remarks were widely condemned as a threat to carry out war crimes but Trump doubled down on his threat while flying back to the White House on Sunday after a two-week stay at his Mar-a-Lago resort in Palm Beach, Fla.

“They’re allowed to kill our people,” Trump told reporters . “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.”

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Trump’s threat was amplified by his supporters on Fox News.

“I don't care about Iranian cultural sites, and I'll tell you why . . . If Iran could — if you understand the Islamic Republic of Iran, of Islamists— if they could, if they had the power, they would destroy every single one of our cultural sites and build a mosque on top of it,” host Pete Hegseth said Monday . “If you don't understand the nature of our enemy, you're foolish about who you're pointing out and whether or not you're happy that Soleimani is dead.”

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But even close Trump ally Sen. Lindsey Graham, R-S.C., rebuked the threats.

“We’re not at war with the culture of the Iranian people,” Graham told The Times. “I think the president saying, 'We will hit you hard’ is the right message. Cultural sites is not hitting them hard; it’s creating more problems. We’re trying to show solidarity with the Iranian people.”

Democrats warned that attacks on cultural sites in Iran, which is home to 22 cultural sites designated on the World Heritage List by UNESCO, would embolden bad actors to do the same.

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“America is better than that, and President Trump is flat-out wrong to threaten attacks on historic places of cultural heritage,” Sen. Jack Reed, D-R.I., said. “Destroying some of these culturally significant Iranian sites wouldn’t be seen as just an attack against the regime in Tehran, it could be construed as an attack on history and humanity.”

Former Homeland Security Secretary Jeh Johnson noted that Trump had threatened to do is what the U.S. repeatedly condemned ISIS for doing.

“We and others accused ISIS of war crimes when they did this,” he told The Times. “Certainly, in aggravated circumstances, it should be considered a war crime.”

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After extensive outcry, the White House attempted to downplay Trump’s comments to suggest he never threatened to attack cultural sites at all.

“He didn’t say he’s targeting cultural sites,” White House adviser Kellyanne Conway told reporters on Monday . “He said that he was openly asking the question why in the world they’re allowed to maim people, put out roadside bombs, kill our people, torture our people.”

While the White House attempted to play clean-up over the president’s tweets, Iranian leader Ayatollah Ali Khamenei instructed his government’s National Security Council to draw up a “direct and proportional attack on American interests” in response to the killing of Soleimani, The Times reported.

“We are ready to take a fierce revenge against America,” Iranian Revolutionary Guard Gen. Hamid Sarkheili said at Soleimani’s funeral Monday. “American troops in the Persian Gulf and in Iraq and Syria are within our reach.”