Protests over an American film ridiculing the Prophet Muhammad spread to a number of countries in the Muslim world, including Yemen, Egypt and Iran — and the demonstration in the Egyptian capital could grow considerably today.

In Yemen’s capital, Sanaa, hundreds of demonstrators penetrated the outer walls of the U.S. Embassy and torched the U.S. flag on Thursday. It was one in a series of attacks or protests targeting U.S. diplomatic missions following Tuesday night’s assault on the U.S. consulate in Benghazi, Libya, where the U.S. ambassador and three other Americans were killed.

In Sanaa, protesters set fire to cars in the embassy compound and burned the U.S. flag, replacing it with a black banner bearing Islam's declaration of faith — "There is no God but Allah."

Yemeni security forces fired warning shots and used tear gas and water cannons to disperse thousands of protesters around the embassy in Sanaa.

No Americans were hurt during the assault. "All embassy personnel are safe and accounted for," U.S. Embassy spokesman Lou Fintor said.

Freelance reporter Iona Craig, speaking to CBC’s News Network from outside the embassy in Sanaa, said the protesters were a mixed group, but united in their anger over the film mocking the Prophet.

"They all see it as an insult against the Prophet Muhammad. Many of them said they would not leave until the filmmaker has been executed, others said they would not leave until the U.S. Embassy had been shut down."

Canada has an honorary consulate in Sanaa, which was not scheduled to be open on Thursday, according to Chris Alexander, parliamentary secretary to the defence minister.

Violent clashes continue in Cairo

In Cairo, meanwhile, protesters clashed with police near the U.S. Embassy for the third day in a row. The demonstration continued into Thursday evening.

Speaking near Cairo's Tahrir Square, CBC News Middle East correspondent Sasa Petricic said a group of perhaps a couple of hundred people exchanged volleys of rocks with police, who blocked the road to the U.S. Embassy near the square. He said larger protests are expected on Friday.

Canada’s Foreign Affairs Department announced that "as a security precaution, and to ensure the protection of Canadian staff, we have closed our embassy in Cairo for the day." The Canadian Embassy, which is on the same street as the U.S. Embassy, will remain closed until at least Sunday.

The department is also monitoring Canadian embassies in other parts of the region, Alexander told CBC's Evan Solomon on Thursday.

"We're looking at arrangements, reviewing them, as you've heard, in Tripoli and elsewhere," he said. "What we're looking for and what we're asking for from all of the governments with whom we work in the region is a clear statement from the highest levels condemning the violence."

An Egyptian protester throws back a tear gas canister toward riot police, outside the U.S. Embassy in Cairo on Thursday. (Nasser Nasser/Associated Press)

A medic in Cairo told CBC's Derek Stoffel at least 250 people were injured in Thursday's clashes, most suffering the effects of tear gas. Al-Jazeera reported dozens were arrested.

Protests could grow in Cairo, where the Islamist Muslim Brotherhood has called for wider demonstrations after Friday prayers.

Egyptian President Mohammed Morsi, speaking while on a visit to Brussels, vowed on Thursday not to allow attacks on foreign embassies in Cairo, saying the Egyptian people reject such "unlawful acts."

Demonstrations also spread to other parts of the Muslim world. Iranian students protested outside the Swiss embassy in Tehran. The embassy there looks after U.S. interests in Iran.

In Iraq hundreds of Shia followers of the anti-American cleric Muqtada al-Sadr demanded the closure of the U.S. Embassy in Baghdad because of the film. Protesters burned American flags and carried banners reading, "We reject the attack on the Prophet Muhammad."

In Dhaka, the capital of Bangladesh, about 1,000 Muslim men gathered in front of the National Mosque and demanded an apology from the U.S. for the controversial video.

Google blocks video in Egypt, Libya

The notorious film ridiculing the Prophet Muhammad, Innocence of Muslims, came to attention in Egypt after its trailer was dubbed into Arabic and posted on YouTube.

The filmmaker initially described himself as an Israeli-born Jew, Sam Bacile, but U.S. federal authorities identified him Thursday as Nakoula Basseley Nakoula, an Egyptian Coptic Christian based in California.

Google rejected demands to remove the video from YouTube, saying it remained within its guidelines. "However, given the very difficult situation in Libya and Egypt, we have temporarily restricted access in both countries."

Afghanistan President Hamid Karzai cancelled an official visit to Norway amid the growing unrest.

Karzai has condemned the anti-Islam film as "inhuman and insulting" and made by "extremists." On Wednesday, the Afghan government temporarily blocked access to YouTube to prevent people from watching the video.

The Taliban have called on their fighters to avenge the film by increasing their attacks on foreign troops in Afghanistan.

Speaking in Washington, D.C., U.S. Secretary of State Hillary Clinton called the video "disgusting and reprehensible."

"The United States government had absolutely nothing to do with this video. We absolutely reject its content and message," said Clinton.

"Our country does have a long tradition of free expression, which is enshrined in our constitution and in our law. We do not stop individual citizens from expressing their views no matter how distasteful they may be. There are of course different views around the world about the outer limits of free speech and free expression. But there should be no debate about the simple proposition that violence in response to speech is not acceptable."

U.S. President Barack Obama on Thursday reiterated his vow to "bring to justice" those who launched the Benghazi assault.

"I want people around the world to hear me, to all those who would do us harm: no act of terror will go unpunished," he said at a campaign event in Golden, Colorado.