Roughly 750 additional American troops will deploy to the region immediately, Secretary of Defense Mark Esper said late Tuesday. “This deployment is an appropriate and precautionary action taken in response to increased threat levels against U.S. personnel and facilities,” he said. The troops are likely to deploy to Kuwait.

Mr. Trump has long called for an end to American conflicts in the Middle East, but has been reluctant to pull troops from the region despite his remarks on the campaign trail.

Secretary of State Mike Pompeo spoke by telephone with Mr. Abdul Mahdi and President Barham Salih in separate calls, and “made clear the United States will protect and defend its people,” according to a summary of the call from the State Department. It said that the Iraqi leaders “assured the secretary that they took seriously their responsibility” to safeguard American officials and property.

The State Department said that American personnel were safe and that there were no plans to evacuate the embassy. The ambassador, Matt Tueller, had been traveling and was not at the embassy when it was breached on Tuesday.

The American airstrikes on Sunday have resulted in the most serious political crisis in years for the United States in Iraq, stoking anti-Americanism and handing an advantage to Iran in its competition for influence in the country.

The airstrikes targeted an Iranian-backed Iraqi militia, Kataib Hezbollah, which the United States accused of carrying out a missile attack on an Iraqi military base that killed an American contractor and wounded American and Iraqi service members. A spokesman for the militia denied involvement in the attack.