SANAA, Yemen - As violence outside U.S. embassies spread to new Arab capitals Thursday, two former U.S. ambassadors said the slow response Tuesday by Egyptian security officials in Cairo points to a security lapse that warrants investigation.

Tear gas was used on protesters outside the U.S. Embassy in Cairo on Thursday while anti-American demonstrators battled police outside the U.S. Embassy in Yemen's capital of Sanaa. The protesters were angered over an anti-Muslim film produced in the USA.

In Benghazi, Libya, where an attack on the U.S. Consulate killed Ambassador Chris Stevens, Libyan guards were clearly overwhelmed by the heavily armed militants who confronted them, but Libyan government forces arrived later that night and fought to regain control of consulate compound.

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Three other Americans -- information management officer Sean Smith and private security guards Glen Doherty and Tyrone Woods -- were also killed in the attack.

The government response in Libya "was a lot different" than in Egypt, "and they abjectly apologized" afterward, said Robert Jordan, ambassador to Saudi Arabia in 2003 when three Western compounds were bombed in Riyadh.

"These demonstrators seemed to be running amok for a while" before the Cairo embassy wall was breached, said Tom McDonald, ambassador to Zimbabwe in 1998, when U.S. embassies in nearby Kenya and Tanzania were bombed. "It begs the question, where were the Egyptian security forces that by law and treaty were supposed to provide security?"

When calls for help go unanswered, "it could be either disorganization (in the host country) or a decision not to provide it," Jordan said.

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The State Department declined to provide more details about when U.S. diplomats in Egypt and Libya asked for assistance and when it arrived. The FBI is investigating rampages in Yemen and Libya, the Justice Department said.

House Intelligence Committee Chairman Mike Rogers, R-Mich., said Thursday that the attack in Libya took American officials by surprise and that there was no advance information that the consulate was a target. Rogers said the timing, tactics and heavily armed gunmen bore all the hallmarks of al-Qaeda.

State Department spokeswoman Victoria Nuland said security officers evaluated threats in Benghazi prior to the 9/11 anniversary "and we determined that the security at Benghazi was appropriate for what we knew."

Wanis el-Sharef, eastern Libya's deputy interior minister, said Thursday the attackers in Benghazi used the protests against the film as cover for their attack. The short trailer to the movie, Innocence of Muslims, posted on YouTube depicts Islam's prophet Mohammed as a fraud and a womanizer.

El-Sharef said four people were arrested at their homes Thursday, but he refused to give any further details. Libya's new prime minister, Mustafa Abu-Shakour, said authorities were looking for more suspects.

Meanwhile, in Sanaa on Thursday morning, black smoke billowed up from a burning SUV inside the U.S. Embassy compound. Hundreds of angry demonstrators tried to storm the building, chanting, "Death to America!" Protesters marched on the embassy from three sides before being blocked by Yemeni security forces. Some demonstrators were able to breach the security cordon.

"They brought this on themselves," Abdullah Rahman Safi shouted above the sound of gunfire. "We want to close the American Embassy for this insult on prophet Mohammed."

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

The protests were taking place around the Tahrir Square area -- the heart of last year's revolution that led to the ouster of dictator Hosni Mubarak and close to the U.S. Embassy.

Protesters were initially primarily hard-line Muslims, but since Wednesday evening the composition of the crowd seemed to change and police battled young men aligned with a group called "Ultras" -- composed of soccer fans who are growing more political.

Secretary of State Hillary Rodham Clinton sharpened her criticism of the film Thursday, calling it "disgusting and reprehensible" and a cynical attempt to offend people for their religious beliefs. However, Clinton said the U.S. would never stop Americans from expressing their views, no matter how distasteful.

Contributing: Kevin Johnson in Washington. Dorell reported from McLean, Va.; Lynch from Cairo.