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.

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