Protesters angered by a film they consider blasphemous to Islam have stormed the U.S. Embassy compound in Yemen's capital, Sanaa, in the most recent attack on U.S. diplomatic posts in the Middle East.

Protesters smashed windows as they breached the embassy perimeter and reached the compound grounds, although they did not enter the main building housing the offices. Angry young men brought down the U.S. flag in the courtyard, burned it and replaced it with a black banner bearing Islam's declaration of faith — "There is no God but Allah."

Yemeni security forces who rushed to the scene fired in the air and used tear gas to disperse the demonstrators, driving them out of the compound after about 45 minutes and sealing off the surrounding streets. It was not immediately clear whether anyone was inside the embassy at the time of the attack.

Demonstrators removed the embassy's sign on the outer wall, set tires ablaze and pelted the compound with rocks.

Yemeni President Abed Rabbo Mansour Hadi ordered an investigation into the attack.

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Hadi avowed to bring the culprits to justice, saying the attack by a "rowdy crowd" was part of a conspiracy to derail Yemen's close relations with Washington.

The Embassy of the Republic of Yemen in Washington, D.C. said in a statement obtained by Fox News that Yemen strongly condemned the attack on the U.S. compound, but says the situation is under control.

"Fortunately no casualties were reported from this chaotic incident. The government of Yemen will honor international obligations to ensure the safety of diplomats and will step up security presence around all foreign missions," the statement said. "We strongly urge all those that would wish to incite others to violence to cease immediately.

Pentagon officials tell Fox News that Pentagon and U.S. Navy officials are monitoring the situation in Yemen, but so far have received no request for military assistance there following the Embassy breach.

"We are doing everything we can to support our mission in Yemen," a senior administration official told Fox News. "We've had good cooperation from the Yemeni government which is working with us to maintain order and protect our facilities and people."

The movie cited in the attacks, "Innocence of Muslims," came to attention in Egypt after its trailer was dubbed into Arabic and posted on YouTube. The video-sharing website blocked access to it Wednesday. The trailer depicts Muhammad as a fraud, a womanizer and a madman in an overtly ridiculing way, showing him having sex and calling for massacres.

The Yemen incident was similar to an attack on the U.S. Embassy in the Egyptian capital of Cairo on Tuesday night. A mob of Libyans also attacked the U.S. consulate in the eastern city of Benghazi on Tuesday, killing American Ambassador Chris Stevens and three other Americans.

Three diplomats injured in the Libyan attack are being treated at an American military hospital in Germany and one of the two most seriously wounded is expected to leave the intensive care unit on Thursday

A State Department status report obtained by The Associated Press says the third injured staffer is awake and alert at the Landstuhl Regional Medical Center near the Ramstein Air Base, where 33 uninjured consulate personnel are staying and receiving military counseling. All were evacuated from Benghazi early Wednesday and arrived in Germany late that afternoon along with the remains of the four diplomats.

According to the report, the injured staffers "are doing relatively well" and most want to return to Libya.

In Iraq, several hundred Shiite hardliners protested in Baghdad's Shiite stronghold of Sadr City. The leader of an Iranian-backed Shiite militia that previously attacked U.S. troops, Asaib Ahl al-Haq, threatened anti-U.S. attacks.

The movie "will put all the American interests in Iraq in danger," the militia leader, Qais al-Khazali, told The Associated Press.

The warning capped a day of growing tensions in Baghdad, where hundreds of Shiite followers of the anti-American cleric Muqtada al-Sadr demanded the closure of the U.S. Embassy in Baghdad over the anti-Islam movie.

Protestors burned American flags and carried banners reading, "We reject the attack on the Prophet Mohammed."

"No, no, to Israel! No, no to America!" thousands shouted in the Shiite stronghold of Sadr City in northeast Baghdad. "Yes, yes for Messenger of God!"

There was no immediate response Thursday from the U.S. Embassy in Baghdad.

In Iran, about 50 protesters shouted, "Death to America," outside the Swiss Embassy, which looks after U.S. diplomatic interests in Iran. Riot police kept the crowd away from the building.

On Thursday, Egyptian protesters also clashed with police near the U.S. Embassy in Cairo for the third day in a row. Police used tear gas to disperse the protesters and the two sides pelted each other with rocks. But unlike Tuesday, the police kept the protesters away from the embassy's compound.

The Interior Ministry, which is in charge of police, said 16 protesters and 13 policemen were wounded in the clashes, which broke out overnight and were ongoing. Twelve protesters have been arrested, it said.

Egyptian President Mohammed Morsi criticized the movie Thursday during a visit to the European Union in Brussels.

"We condemn strongly ... all those who launch such provocations and who stand behind that hatred," Morsi said, adding that he had asked Obama "to put an end to such behavior."

But Morsi also urged the Egyptian people to not engage in "unlawful acts."

The Associated Press contributed to this report.