Washington(CNN) The Pentagon issued a strong warning to Iran-backed militias amid concerns they may conduct further provocations against the US following their attempt to storm the US embassy in Baghdad.

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

The US recently reinforced the embassy in the Iraqi capital with a contingent of US Marines and has deployed hundreds of additional troops to neighboring Kuwait that could be called upon if the situation deteriorates.

Demonstrators appeared to attempt the embassy this week following US airstrikes against a militia, Khatib Hizbollah, which while ostensibly part of the Iraqi security forces is seen by the US as having close ties to Iran and the US accuses them of conducting a series of rocket attacks against US-Iraqi military facilities, one of which killed a US citizen working as a contractor.

Milley added that the groups that protested outside the US embassy were mostly members of the same militia group that has conducted the rocket attacks which he called a "sustained campaign" that "has increased in tempo and intensity." The Pentagon has accused Iran and its Islamic Revolutionary Guard Corps of directing the attacks.

"The guys who were doing it were KH, half of those guys were in uniform, they had a command post set up and all that and they were throwing Molotov cocktails, making flames, doing smoke all that kind of business in order to get lots of attention which they did," he said.

Speaking alongside Milley, Secretary of Defense Mark Esper said he thinks Iranian backed forces "may do" additional provocations against US interests and if they do, "they will likely regret it, and we are prepared to exercise self-defense and we are prepared to deter further bad behavior from these groups all of which are sponsored, directed and resourced by Iran."

He also said the US "will take preemptive action as well" if they detect an attack is imminent.

Esper called on Iraq to do more to secure the US embassy as well as help respond to and prevent the militia's attacks on US-Iraqi military facilities.

Many questioned how the demonstrators were able to get so close to the US embassy compound guarded by local Iraqi security forces who appeared to make no effort to block the militia members from approaching.

"The Iraqis have a responsibility to the United States and all countries who have embassies in that country to defend, provide the outer security for the embassy and we expect them to do that. That was communicated to them by our senior leaders, by Secretary Pompeo and they've committed to doing that. I think their performance has greatly improved in the last 24 hours," Esper said.

"I've made the point over and over again that they need to do more internally within Iraq to address these Iran sponsored militia groups and stop their attacks on US and coalition forces and they need to investigate the attacks and help us to account the preparators, we haven't seen sufficient action on their part and they certainly need to help reinforce and defend the embassy but they need to get left of the problem and stop these attacks from happening and they get the Iranian influence out of their country," he added.

Members of the militia group and their political allies in Iraq's parliaments have called on the government of Iraq to expel US forces from that country.

Esper said he has received to requests from Iraq to downsize the US military presence in Iraq, currently at about 5,000 troops.