Protests inspired by an anti-Islam film targeted more U.S. facilities in the Muslim world Thursday, testing the will and capacity of foreign governments to protect Americans and the ability of the Obama administration to cool the growing anger.

As the anti-U.S. demonstrations spread, the administration acted on a variety of fronts to convey two messages: that it had nothing to do with the offending video and that violence was not an acceptable response to the material.

The impact of the administration’s message remained in question. In Sanaa, Yemen, the U.S. Embassy was overrun Thursday by protesters who stormed a wall, set fire to a building inside the compound, broke windows and carried away office supplies and other souvenirs before being dispersed by local security forces.

“We want to expel the American ambassador,” Abdelwadood al-Mutawa said as he and other protesters left the compound. He said he was motivated by reports of the movie mocking the prophet Muhammad. “We cannot accept any insult to our prophet,” Mutawa said. “It’s a red line.”

In Cairo, clouds of tear gas floated through the fortified area around the U.S. Embassy as security forces clashed with protesters for the third straight day. Smaller demonstrations were reported throughout the region, as well as in Iran and Bangladesh.

In Pakistan, where anti-American demonstrations are frequent, the government said it had “banned” the American-made video and blocked access to it online. Although Afghanistan reportedly did the same, “Innocence of Muslims” was easily available there on the Internet on Thursday night.

Two days after the deaths of J. Christopher Stevens, the U.S. ambassador to Libya, and three other Americans in an outbreak of violence in the Libyan city of Benghazi, Secretary of State Hillary Rodham Clinton took the lead in trying to distance the U.S. government from the movie, calling the film “disgusting and reprehensible” and condemning the violent response to it.

“The U.S. government had absolutely nothing to do with this video,” Clinton said at a meeting in Washington with a delegation from Morocco. “We absolutely reject its content and messages. But there is no justification — none at all — for responding to this video with violence.”

The message went out from Washington throughout the day, in White House briefings, in speeches in Arab capitals and through official Web sites, e-mails and Twitter feeds from the State Department and its embassies around the globe.

Some governments responded to U.S. calls for strong statements against violence. After days of relative silence, Egyptian President Mohamed Morsi, speaking during a visit to Brussels, condemned the attacks on the embassy in Cairo and vowed to defend the security of U.S. diplomatic buildings.

But Morsi also denounced the film and called on “the American people” to “declare their rejection” of such provocations.

A protest called for by Morsi’s Muslim Brotherhood movement on Friday unfolded peacefully, with demonstrators gathering in Tahrir Square without incident. Reflecting worry from influential Egyptian political and clerical leaders that the tone of demonstrations had gotten too heated, the ultraconservative Nour political party said Thursday that the demonstrations should take place away from embassies and condemned both violence and the video.