Baghdad — An estimated 6,000 angry Iraqi protesters gathered at the U.S. Embassy in Baghdad on Tuesday, railing against deadly U.S. airstrikes this week that killed 25 fighters from an Iran-backed Shiite militia in Iraq. Shouting "Down, Down USA!," several dozen managed to get into what a senior U.S. official described to CBS News as a reception area just outside the compound after scaling a wall.

The U.S. official told CBS News' Margaret Brennan that many of the protesters were in fact violent actors sent by the Iranian-linked militias. The official denied reports that the heavily fortified embassy compound was breached. Videos posted to social media showed a group of at least two dozen crammed into a courtyard area inside the main gate, bashing on windows and doors trying to get into the compound.

The U.S. is sending more troops to protect the embassy compound, the Pentagon and State Department said. A U.S. defense official told CBS News correspondent David Marin the military is sending reinforcements to the embassy from units already in country.

Get Breaking News Delivered to Your Inbox

Defense Secretary Mark Esper said the U.S. has taken actions to "ensure the safety of American citizens, military personnel and diplomats" and to "ensure our right of self-defense. We are sending additional forces to support our personnel at the Embassy."

"U.S. personnel are secure," added an official from the State Department. "There are no plans to evacuate Embassy Baghdad."

The large crowd earlier tore down security cameras and torched at least one guard post on the perimeter.

The U.S. military carried out the strikes Sunday against the Iranian-backed Kataeb Hezbollah militia, calling it retaliation for last week's killing of an American contractor in a rocket attack on an Iraqi military base that it blamed on the group.

Iran killed an American contractor, wounding many. We strongly responded, and always will. Now Iran is orchestrating an attack on the U.S. Embassy in Iraq. They will be held fully responsible. In addition, we expect Iraq to use its forces to protect the Embassy, and so notified! — Donald J. Trump (@realDonaldTrump) December 31, 2019

The U.S. attack — the largest targeting an Iraqi state-sanctioned militia in recent years — and the militia's vow to retaliate, represented a new escalation in the proxy war between the U.S. and Iran playing out in the Middle East. President Donald Trump tweeted early Tuesday to defend the U.S. airstrikes and warn that Iran would be held responsible for "orchestrating an attack on the U.S. Embassy in Iraq."

"In addition, we expect Iraq to use its forces to protect the Embassy, and so notifie

U.S. Secretary of State Mike Pompeo spoke early Tuesday to Iraq's caretaker Prime Minister Adil Abdul-Mahdi and "made clear the United States will protect and defend its people, who are there to support a sovereign and independent Iraq," according to a statement by department spokesperson Morgan Ortagus.

Ortagus said Iraq's leaders had "assured the Secretary that they took seriously their responsibility for and would guarantee the safety and security of U.S. personnel and property."

Members the Hashed al-Shaabi, a mostly Shiite network of local armed groups trained and armed by Iran, smash bullet-proof glass doors of the U.S. Embassy's reception hall in Baghdad after breaching the outer wall of the diplomatic mission on December 31, 2019. AHMAD AL-RUBAYE/GETTY

The senior U.S. official who spoke to CBS News' Brennan on Tuesday said the Iraqi security forces responsible for perimeter security at the American embassy were at best "late" in their response to what were planned protests by the Iranian-supported militias.

Videos posted on social media showed the crowd outside the embassy growing as smoke billowed from at least one guard checkpoint on the perimeter of the compound. Iraqi special forces responded, firing tear gas to try and disperse the protesters. Social media videos showed U.S. troops inside the compound — including several who appeared to be separated from the protesters by only a pane of glass.

Due to ongoing protest activity, U.S. citizens should not approach the U.S. Embassy in Baghdad. Americans should review... Posted by U.S. Embassy Baghdad on Tuesday, December 31, 2019

The Reuters news agency reported that U.S. Ambassador to Iraq Matthew Tueller and members of his staff were evacuated from the heavily fortified compound for safety reasons as the protests raged, but U.S. and Iraqi officials told CBS News on Tuesday that Tueller had already left Baghdad on holiday leave before the embassy protests erupted. U.S. officials denied that there was an evacuation of the embassy.

Several senior Iraqi officials came to the embassy compound Tuesday to try and calm the protesters. In a statement posted to his official Facebook account, caretaker Prime Minister Adel Abdul Mahdi urged them to disperse and warned that "any aggression or harassment towards a foreign embassy or mission is an act that will be firmly dealt with by Iraqi security forces, and will be severely punished by the law."

Mahdi said his government had condemned the U.S. airstrikes "at the highest levels, and the government took a series of measures to address the situation in a way that secures the sovereignty of Iraq and the security of its citizens."

The dramatic events Tuesday at the embassy took place after mourners held funerals for the militia fighters killed in a Baghdad neighborhood, after which they marched to the heavily fortified Green Zone and kept walking until they reached the sprawling U.S. Embassy compound there.

Security guards were seen retreating to the inside of the embassy. Protesters also were seen hanging yellow flags belonging to the Kataeb Hezbollah militia backed by Iran on the walls of the embassy.

Pompeo said the strikes send the message that the U.S. will not tolerate actions by Iran that jeopardize American lives.

The U.S. attack outraged both the militias and the Iraqi government which said it would reconsider its relationship with the U.S.-led coalition — the first time it has said it will do so since an agreement was struck to keep some U.S. troops in the country. It called the attack a "flagrant violation" of its sovereignty.

In a partly televised meeting Monday, Prime Minister Mahdi told Cabinet members that he had tried to stop the U.S. operation "but there was insistence" from American officials.

The U.S. military said "precision defensive strikes" were conducted against five sites of Kataeb Hezbollah, or Hezbollah Brigades in Iraq and Syria. The group, which is a separate force from the Lebanese militant group Hezbollah, operates under the umbrella of the state-sanctioned militias known collectively as the Popular Mobilization Forces. Many of them are supported by Iran.

The U.S. maintains some 5,000 troops in Iraq, at the invitation of the Iraqi government to assist and train in the fight against the Islamic State of Iraq and Syria (ISIS).

The attack that killed the American contractor and U.S. counter-strikes come as months of political turmoil roil Iraq. About 500 people have died in anti-government protests, most of them demonstrators killed by Iraqi security forces.

The mass uprisings prompted the resignation last month of Prime Minister Adel Abdul-Mahdi, who remains in a caretaker capacity.