President Abdrabuh Mansur Hadi apologised to his US counterpart Barack Obama and the American people for the acts of a "mob" and ordered a probe into the attack, Saba state news agency said.[break]
"Those who are behind (the attack) are a mob that are not aware of the far-reaching plots of Zionist forces, especially those of made a film insulting the prophet," said Hadi.
All protesters who breached the fence of the US mission in Sanaa were ejected by security forces, who used water cannon and fired warning shots, the correspondent reported.
Some protesters said they saw three vehicles being torched by some of the demonstrators who crossed the first gate where a security kiosk was empty.
Police fired warning shots earlier to disperse thousands of protesters as they approached the main gate of the mission.
"O, messenger of Allah... O, Mohammed!" demonstrators chanted.
After being evicted from the complex, protesters retreated about 100 metres (yards) from the gate, gathering near a checkpoint where they chanted anti-Jewish slogans.
"O, Jews: Khaybar, Khaybar. The army of Mohammed will return," they chanted evoking a 7th century war in the west of the Arabian Peninsula in which the Muslims are said to have defeated the Jews.
The attack comes two days after four Americans, including the ambassador, were killed when a Libyan mob attacked the US consulate in Benghazi, and protesters in Cairo tore down the Stars and Stripes and replaced it with a black Islamic flag.
Libya has launched an inquiry into the Benghazi attack, amid growing speculation that Al-Qaeda militants among the frenzied mob carried out the assault rather than simple demonstrators.
On Thursday, protesters were back outside the US mission in Cairo. Police used tear gas as they clashed with a stone- and bottle-throwing crowd.
Protests against the film were also held on Wednesday outside US missions in Morocco, Sudan and Tunisia. In Tunis, police fired tear gas to disperse a crowd of several hundred.
In other Muslim countries, security measures have tightened around US missions. Several governments tried to block internet access to the controversial film.
The low-budget movie "Innocence of Muslims," in which actors have strong American accents, portrays Muslims as immoral and gratuitously violent.
It pokes fun at the Prophet Mohammed and touches on themes of paedophilia and homosexuality, while showing him sleeping with women, talking about killing children and referring to a donkey as "the first Muslim animal."
Mystery has deepened over the film, with conflicting accounts from backers and promoters but no one owning up to having actually directed it.
US media initially cited someone claiming to be an American-Israeli and calling himself Sam Bacile as saying he made the film on a $5 million budget with the help of 100 Jews, but no record of such a person has been found.
Coptic Christians have been accused of promoting an Arabic-adapted version of the English-language film in Egypt, where clips were shown on an Egyptian television channel at the weekend, apparently setting off the protests.
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