In a statement on his official Facebook page, Egypt's Islamist president, Mohammed Morsi, condemned the movie, saying the government was responsible for protecting diplomatic missions as well as the freedom of speech and peaceful protest.
But, he added, authorities "will confront with full determination any irresponsible attempt to break the law."
Romney's criticism of Obama didn't mesh completely with events in Cairo.
A U.S. Embassy statement that Romney referred to as akin to apology was issued by the Cairo embassy at midday on Tuesday at a time the staff was aware of still-peaceful demonstrations nearby. It was four or five hours later when the mob breached the compound's walls and tried to burn a U.S. flag, and later still when the Libya attack happened.
The embassy statement condemned "the continuing efforts by misguided individuals to hurt the religious feelings of Muslims — as we condemn efforts to offend believers of all religions," and noted that religious freedom is a cornerstone of American democracy.
About 50 protesters burned American flags outside the U.S. Embassy in Tunisia's capital Wednesday but were kept away from the building by reinforced security. And in Gaza City, dozens of protesters carrying swords, axes and black flags chanted "Shame on everyone who insults the prophet." The rally was organized by supporters of a militant group aligned with the ruling Hamas movement.
Afghanistan's government sought to avert any protests. President Hamid Karzai condemned the movie, and authorities also temporarily shut down access to YouTube, said Aimal Marjan, general director of Information Technology at the Ministry of Communications.
A man identifying himself as Sam Bacile, a 56-year-old California real estate developer, said he wrote, produced and directed the movie.
He told the AP he was an Israeli Jew and an American citizen. But Israeli officials said they had not heard of Bacile and there was no record of him being a citizen. They spoke on condition of anonymity because they are not permitted to share personal information with the media.
Separately, the film was being promoted by an extreme anti-Muslim Egyptian Christian campaigner in the United States.
Michael reported from Cairo. Associated Press writer Esam Mohamed in Tripoli, Matthew Lee in Washington, Joseph Federman in Jerusalem and Sarah El Deeb in Cairo contributed to this report.
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