Six police officers suffered minor injuries during the clashes, said Alla Mahmoud, a spokesman for the Egyptian Interior Ministry. Some protesters received medical treatment inside ambulances.
Demonstrators threw rocks and Molotov cocktails as police tried to disperse them by firing tear gas canisters from police vehicles as they drove through Tahrir Square, near the embassy.
The clashes came amid heightened tensions at U.S. diplomatic missions in the region following Tuesday's attack on the U.S. Consulate in Benghazi, Libya, that left Ambassador to Libya Chris Stevens and three other consular officials dead.
On Tuesday, the 11th anniversary of the 9/11 terrorist attacks, several men scaled the walls of the U.S. Embassy in Cairo and tore down its U.S. flag.
About 500 protesters turned out Wednesday in Cairo to demonstrate against a film that mocks Islam's prophet.
Wednesday night's protest turned violent as demonstrators threw rocks and pushed through barbed wire fencing outside the embassy, according to Mahmoud. Two police trucks and a car were set afire.
"Forces were able to push them down toward Tahrir Square farther from embassy street," Mahmoud said, adding that some arrests had been made.
Many of the protesters chanted anti-U.S. slogans. By early Thursday, protesters had been pushed 100 yards from the embassy, said journalist Ian Lee in Cairo.
More than a dozen people were injured in the clashes, which continued after midnight, said Khaled Khatib of the Health Ministry.
Earlier, Egypt's president spoke in the "strongest terms" about Tuesday's incident at the Cairo embassy -- but not against the attack.
WhiIe Egypt's prime minister called Tuesday's incident "regrettable" and unjustified, President Mohamed Morsy condemned the anti-Muslim film that incited the protesters.
Morsy made a reference to Egypt's duty to protect diplomatic missions and its opposition to unlawful protesters, but did not mention those who stormed the embassy.
"The presidency condemns in the strongest terms the attempt of a group to insult the place of the Messenger, the Prophet Mohammed (PBUH) and condemns the people who have produced this radical work," the president said in a statement posted on his Facebook page. "The Egyptian people, both Muslims and Christians, refuse such insults on sanctities."
The statement noted that "the Egyptian government is responsible to protect private and public properties and diplomatic missions in addition to embassy headquarters of various countries" and that "it respects and protects the right of expression and the right to protest peacefully under the law and will firmly oppose any irresponsible attempt to veer off the law."
Tuesday, police and Egyptian army personnel formed defensive lines around the U.S. Embassy to prevent demonstrators from advancing, but not before the protesters had affixed a black flag atop a ladder in the American compound.
The flag was adorned with white characters that read, "There is no God but Allah and Mohammed is his messenger," a phrase often used by Islamic radicals.
Warning shots were fired as a crowd gathered around the compound, although it was not clear who fired the shots. There were no reported casualties.
Four protesters were arrested and were being questioned for "going off track to what is accepted as peaceful protesting," said Interior Ministry spokesman Alla Mahmoud.
The Cairo incident was not nearly as bad as the violence in neighboring Libya, where an attack on the U.S. Consulate in Benghazi killed four Americans, including Stevens. The Libya attack has been blamed on a pro-al Qaeda group, according to sources tracking militant groups in the region.
It was unclear if the two attacks were coordinated. Protesters in both countries were upset over an online film that depicts Islam as a fraudulent religion and the Prophet Mohammed as a womanizer, child molester and ruthless killer.
In his statement, Morsy called on Egyptian diplomats in Washington "to take legal action against those people who seek to ruin relationships and discussions between people and countries."
The incident comes amid a delicate period in the relationship between the United States and Egypt under Morsy, the country's first leader since the overthrow last year of longtime ruler Hosni Mubarak, a key Western ally.
Embassy officials issued a warning to Americans in Egypt, telling them to avoid the demonstrations.
Frenzied protesters could be seen Tuesday afternoon holding up bits of a shredded American flag to television camera crews while chanting anti-U.S. slogans.
"This is an expression of a feeling that is thought to be an insult," said Nizih El Naggary, a spokesman for the Egyptian Foreign Ministry. "But events like this are extremely deplorable. And we have to work to get things under control."
Egypt's Foreign Ministry pledged to protect embassies and warned of the protests' potentially debilitating effects on the Egyptian economy.
Several individuals claimed responsibility for organizing the demonstrations, including Salafist leader Wesam Abdel-Wareth, president of Egypt's conservative Hekma television channel.
Demonstrations elicited a mixture of reactions from the Egyptian street, where last year tens of thousands turned out in opposition to Mubarak.
"These protests are a bad image for Egypt," said Ahmed, a Cairo street vendor. "Of course I'm against insulting Islam, but it's the undereducated, poor people who are out here causing problems."
"All I want for Egypt is security and stability," he said. "And as you can see this isn't it."
CNN's Mohamed Fadel Fahmy and Ian Lee in Cairo, Jomana Karadsheh, Matt Smith, Brian Walker, Elise Labott, Paul Cruickshank and Tracy Doueiry contributed to this report
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