Highlighting the challenge facing President Mohamed Mursi, protesters threw stones at police blocking their approach to the fortress-like embassy near Tahrir Square, even as his televised address was broadcast on Thursday.
Police fired tear gas back.
Hundreds of demonstrators had gathered in the area, but a smaller group of those joined battles with police.
The health ministry said 224 people were injured, according to the state news agency, and 23 people were detained.
Many Muslims believe depicting the Prophet is blasphemous. In the past, cases where the Prophet was insulted have stirred condemnation and protests across the Islamic world.
"Expressing opinion, freedom to protest and announcing positions is guaranteed, but without assaulting private or public property, diplomatic missions or embassies," said Mursi, an Islamist who is Egypt's first freely elected President.
He pledged to protect foreigners in Egypt, a comment he repeated during a news conference in Brussels where he was making his first European trip to build ties with European Union states and secure support for Egypt's embattled economy.
The EU offered Egypt economic aid of up to 700 million euros ($902.19 million), following Arab Gulf states and the US pledging support for the country's battered economy.
The US embassy assault will test Mursi's handling of ties with the West and particularly the United States, a close ally of Egypt under ousted President Hosni Mubarak and which has long been wary of Islamists.
Washington is a major aid donor to Cairo.
Mubarak was toppled in popular protests last year.
US President Barack Obama told a Spanish-language network that Egypt's Islamist-led government should not be considered a US ally "but we don't consider them an enemy."
US secretary of state Hillary Clinton said the film was "disgusting" and that the US government had nothing to do with it.
Mursi also needs to strike a balance by addressing the anger over a film that portrayed the Prophet as a philanderer and religious fake, enraging Muslims across the region.
Call for US action
The US ambassador to Libya and three other staff were killed when the US consulate in Benghazi was attacked on Tuesday. Since then, police have fired tear gas at protesters in Tunisia and demonstrators stormed the US mission in Yemen.
"All of us Egyptians reject any form of attack or insult to the Prophet," Mursi said, while offering his condolences over the killing of the US ambassador and diplomats in Libya.
Mursi said he had spoken to Obama on Thursday.
"I affirmed to him the need for deterrent legal measures against those who want to damage relations between peoples, and particularly between the people of Egypt and the people of America," he said.
In another statement, Mursi said he expects "assurances from the US government to prevent any infringement on the sacred".
At least one of the promoters of the film Innocence of Muslims is an Egyptian Coptic Christian who lives in America. Clips of the film have circulated on the internet for weeks.
The clashes flared in Cairo on Wednesday and protesters hurled rocks at police and dodged teargas canisters again on Thursday.
Interior minister Ahmed Gamal el-Din visited the scene, the state news agency reported.
The US embassy in Cairo was closed for public business again on Thursday.
In a security message on its website, the embassy urged US citizens in Egypt to be vigilant and said they should "avoid areas where large gatherings may occur".
The embassy is close to Tahrir, the cauldron of the anti-Mubarak protests and scene of many protests since. Streets around the square have often become battlegrounds with police.
Mixture of protesters
Washington has a big mission in Egypt, partly because of a huge aid programme that followed Egypt's signing of a peace treaty with Israel in 1979.
The United States gives $1.3 billion to Egypt's military each year and offers the nation other aid.
The demonstrators were a mixed crowd. Some were angry at the police for barring the way to the embassy.
A few were Christians who turned up in solidarity with Muslim compatriots. Others said their main goal was to demonstrate against police repression.
The earlier protest included many backers of ultra-orthodox Islamist groups but there was little sign of them on Thursday.
"We came here because of the insult to the Prophet," said Farag Ragheb, 26, clutching stones and fleeing a gas plume.
"We were next to the American embassy in a peaceful protest and the police intervened. Don't we have the right to protest?"
The scene was similar to other street battles, though less intense, since Mubarak fell.
"They are just the same as before," shouted one young man, pointing to the police cordon.
By late afternoon, security has pushed the protesters well away from the embassy and into Tahrir using barrages of tear gas, but several of the youths vowed to stay.
"We want to enter the embassy and pull down the flag and kick out the ambassador," said 25-year-old unemployed graduate Alaa el-Din Yehia.
A few who were asked said they had seen clips of the film. Several said they had not seen it and did not know its name. Some said it would be wrong to watch the film at all.
The Coptic Orthodox church and Egypt's highest seat of Islamist learning, Al-Azhar, have both condemned the film.