Pentagon leadership confident in security of US Embassy in Baghdad, undecided about additional troop deployments

America's top military officer expressed high confidence in the security of the U.S. Embassy in Baghdad on Thursday, just days after protesters were able to breach the outer wall of the compound.

"We are very confident that the integrity of that embassy is strong," Chairman of the Joint Chiefs of Staff Gen. Mark Milley told reporters at the Pentagon. "And it is highly unlikely to be physically overrun by anyone. There is sufficient combat power there -- air and ground -- that anyone who attempts to overrun it will run into a buzz saw."

The demonstrators, some of whom are part of the Iranian-backed militia Kata'ib Hizbollah (KH), stormed to the embassy on New Year's Eve in opposition to U.S. airstrikes against the group the weekend prior which had been a response to a rocket attack on an Iraqi military base near Kirkuk that killed one American contractor.

In response to the protesters throwing rocks and Molotov cocktails and setting fire to a guard post, the Pentagon surged about 100 Marines to the compound for added security. Then later on Tuesday, Defense Secretary Mark Esper announced that 750 soldiers with the 82nd Airborne Division would deploy to Kuwait -- with thousands more on alert status pending developments in the region.

Esper told reporters on Thursday that the Pentagon is still assessing whether to deploy those additional forces, despite a belief that KH will again respond to the U.S. strikes against them.

"So, do I think they may do something? Yes, and they will likely regret it," Esper said. "And we are prepared to exercise self defense, and we are prepared to deter bad behavior by these groups all of which are sponsored, directed, and resourced by Iran."

In an interview with Fox News later on Thursday, Esper said that response could include taking "preemptive action" if necessary to defend American interests.

On Wednesday, the crowd outside the embassy was dispersed by Iraqi security forces following calls by the Trump administration to protect the diplomatic compound where hundreds of American contractors and personnel are located.

But on Thursday, Esper criticized the Iraqi government for not doing enough to contain Iranian-backed militia groups in the country, also known as Popular Mobilization Units, that continue to attack U.S. and coalition forces. He said the government needs to "double down" on efforts to get the militias under control or out of the country altogether -- an idea which could prove challenging because many Iraqi officials are aligned with Iran and Shiite militias.

The KH attack on the Iraqi base last Friday that killed one American contractor and wounded several U.S. and Iraqi forces was the latest in a string of attacks by the group that the Pentagon says is backed by Iran.

Milley called the attacks a "sustained campaign" by the group against U.S. and coalition forces which had "increased in intensity and tempo" in the last several months.

In a tweet on Tuesday, President Donald Trump said, "Iran will be held fully responsible for lives lost, or damage incurred, at any of our facilities. They will pay a very BIG PRICE! This is not a Warning, it is a Threat. Happy New Year!"

Meanwhile, all public consulate operations at the U.S. Embassy in Baghdad have been suspended with the State Department advising U.S. citizens not to approach the compound.