Speaking to reporters just hours after dozens of Iran-backed Iraqi Shiite militiamen and their supporters broke into the U.S. Embassy in Baghdad, President Trump on Tuesday night vowed that the situation "will not be a Benghazi" -- a pointed reference to the deadly 2012 attack on the U.S. consulate in Libya on the Obama administration's watch, after officials at the compound had requested enhanced security for weeks.

"It's been handled very well," Trump said as he walked into New Year's Eve celebrations at his Mar-a-Lago resort in Florida. "The Marines came in. We had some great warriors come in; they did a fantastic job. They were there instantaneously, as soon as we heard. They came immediately. It's in great shape. This will not be a Benghazi. Benghazi never should have happened. This will never, ever be a Benghazi. ... As soon as we saw there was a potential for a problem, they got in."

Trump added: "Things are in great shape. ... I want to thank the Iraqi government. They really stepped up."

"This will not be a Benghazi. Benghazi never should have happened." — President Trump

Iran, Trump said, "should want peace more than anybody," and any conflict "would go very quickly." But, Trump said he did not see such a fight materializing, even as he unequivocally pointed the finger at Iran for the embassy breach.

Meanwhile, multiple media outlets, including The New York Times, inexplicably opted to describe the embassy attackers simply as "Iraqi mourners."

Separately, Trump told reporters he was not worried about what he called Democrats' impeachment "hoax," pointing out that Ukraine's leader has said he felt no pressure from the White House to launch any political investigations.

Trump slammed House Speaker Nancy Pelosi, D-Calif., as "a highly overrated person" and said he would be happy to have a Senate trial, although he emphasized he didn't really care one way or the other.

The president went on to defend his brief suspension of foreign aid to Ukraine this year -- which Democrats have claimed was an attempt to pressure Ukraine into investigating Joe Biden -- by asking why other countries did not provide anything near the level of foreign aid that the U.S. regularly provided: "Why is it always the United States? Nobody ever covers that, but I think it's a big factor."

The president also said he had a strong relationship with North Korean leader Kim Jong Un, who has signaled he might soon give Trump a Christmas present in the form of renewed missile tests.

"I hope his Christmas present is a beautiful vase," Trump said. "Look, he likes me, I like him. We get along. He's representing his country, I'm representing my country, we have to do what we have to do. But, he did sign a contract, he did sign an agreement talking about denuclearization."

Trump didn't disclose his New Year's resolution, though -- saying he thought those should generally be kept private.

"Happy New Year," Trump said. "We're gonna have a great year."

A U.S. official told Fox News earlier in the day that "Iraqi security forces did participate" in protecting the embassy — and Trump made clear he expected Iraq to secure U.S. personnel.

“[W]e expect Iraq to use its forces to protect the Embassy, and so notified!” Trump wrote in a Tuesday afternoon tweet blaming Iran. He also spoke with Iraqi Prime Minister Adil Abdul-Mahdi, stressing again the need to protect U.S. facilities in Iraq.

Trump explicitly warned Iran on Twitter that the country "will pay a very BIG PRICE!" after the embassy attack. "Iran will be held fully responsible for lives lost, or damage incurred, at any of our facilities," he wrote. "They will pay a very BIG PRICE! This is not a Warning, it is a Threat. Happy New Year!"

BENGHAZI TEAM MEMBER CALLS IRAQ'S RESPONSE TO EMBASSY ATTACK A 'SLAP IN THE FACE'

Militants smashed a main door at the embassy and set fire to a reception area in one of the worst attacks on the embassy in recent years. Fox News has learned more than 100 Marines have arrived at the embassy to bolster security.

Additionally, the U.S. Army’s 82nd Airborne Division’s alert brigade has been issued orders to deploy rapidly to Kuwait amid the unrest in Baghdad, three U.S. defense officials told Fox News. At least 500 paratroopers already were making their way to Kuwait, Fox News was told.

The alert brigade of roughly 4,000 paratroopers, known as the DRB—the Deployment Ready Brigade -- has been told to pack their bags for a possible deployment in the days ahead. Within that alert brigade, three rifle battalions had a certain alert sequence, 18 hours, 36 hours and 54 hours for the third. The entire brigade had a 96-hour alert window to deploy.

Some of the paratroopers already have left their base in Fort Bragg, N.C., to fly overseas in Air Force C-17 cargo planes, according to officials. The U.S. Army, as a matter of course, has kept an alert brigade of roughly 4,000 paratroopers in the 82nd Airborne for crisis response. Roughly 5,000 U.S. troops had been deployed to Iraq, among the roughly 60,000 U.S. troops deployed to the entire region. The Pentagon has added some 14,000 since May as the threat from Iran increased, officials said.

U.S. CARRIES OUT AIRSTRIKES IN IRAQ AND SYRIA AFTER CONTRACTOR IS KILLED

The aircraft carrier USS Harry S. Truman has been in the Gulf of Oman, along with a strike group armed with hundreds of Tomahawk cruise missiles, in addition to the dozens of strike aircraft aboard Truman.

The crowd attacked the embassy following funerals for 25 Iranian-backed fighters killed in U.S. airstrikes Sunday in Iraq and Syria - -retribution for an American defense contractor killed in Iraq Friday, according to U.S. defense officials.

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A U.S. Apache helicopter gunship also flew over the embassy and dropped flares in a “show of force,” attempting to disperse the crowd.

Defense Secretary Mark Esper later confirmed additional forces were being sent, as the military released images of those forces deploying from Kuwait.

Fox News' Lucas Tomlinson and Andrew O'Reilly contributed to this report.