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.

“We appreciate and value . . . the statement from the American embassy that condemned the insult to Islam and its prophets,” the party said in a statement.

Yemeni President Abed Rabbo Mansour Hadi, meanwhile, quickly apologized to the United States for the damage to the embassy in Sanaa and ordered an investigation into the incident.

In a telephone call with Hadi on Thursday, the White House said, President Obama “reiterated his rejection of any efforts to denigrate Islam and emphasized that there is never any justification for the violence we are seeing.”

Clinton spoke alongside Moroccan Foreign Minister Saad-Eddine el-Othmani, who offered condolences for the death of Stevens and the three other State Department employees. He echoed his government’s “clear position against violence and against any confrontation as a way to solve problems and settle conflicts.”

Othmani also thanked Clinton for speaking out against the “insult” of the video.

President Obama spoke by phone with Libyan President Mohamed Yusuf al-Magariaf late Wednesday, accepting condolences for the deaths and expressing appreciation for the cooperation between the United States and Libya in the wake of the attack, the White House said.

Administration officials added little Thursday to accounts of how Stevens died. He became separated from others in the smoke and gunfire of the attack on the U.S. Consulate in Benghazi and was not seen by colleagues until hours later, when Libyans delivered his body to the airport during diplomatic evacuation efforts. State Department spokeswoman Victoria Nuland repeated earlier information that officials were told that Stevens had first been taken from the consulate to the local hospital, but she said they could not confirm that.

“We don’t have any definitive information of our own as to exactly when he passed or what the precise causes of death were,” Nuland said. “I would guess that this is among the things that’ll become clearer as the Libyans work on their investigation with our support.”

The body of one of the other Americans, Sean Smith, was found inside the consulate when U.S. personnel regained control of it early Wednesday. On Thursday night, Clinton issued a statement identifying the two others as Glen A. Doherty and Tyrone S. Woods, both former Navy SEALs who had served in Afghanistan and Iraq and were working as security personnel for the State Department. Clinton said both had “died protecting their colleagues.”

On Capitol Hill, CIA Director David H. Petraeus briefed lawmakers about the Benghazi attack, but according to one person who attended the closed-door session, Petraeus said it remained unclear who was behind the attack, whether it was planned or whether there was evidence pointing to al-Qaeda involvement. The person spoke on the condition of anonymity because of the sensitivity of the session.

At the State Department, Nuland said Clinton “wanted to speak so strongly and so directly” because the government was concerned “that people in the region don’t understand our culture and society, that [the video] was, in fact, a private effort, that it has nothing to do with the U.S. government, that we don’t do these kinds of videos, and that, in fact, as a government, we found it disgusting and reprehensible.”

“I hope all of you will disseminate and broadcast [her message] as broadly as you can,” Nuland told reporters at the daily briefing. Clinton’s remarks were “extremely intentional,” Nuland said, “because we are concerned that this is not understood well.”

In a State Department reception Thursday night to celebrate the Eid holiday marking the end of Ramadan, Clinton told gathered Muslim diplomats and others, “When all of us who are people of faith — and I am one — feel the pain of insults, of misunderstanding, of denigration to what we cherish, we must expect ourselves and others not to resort to violence.”

They and the United States, she said, must “recommit ourselves to working toward a future marked by understanding and acceptance rather than distrust, hatred and fear. We can pledge that whenever one person speaks out in ignorance and bigotry, 10 voices will answer.”

In emotional remarks, Libya’s ambassador to the United States, Ali Aujali, told Clinton and the others of his friendship with Stevens, whom he called “a real hero.” Aujali said it was “our responsibility, and the responsibility of the Libyan people . . . to protect the Americans” and other diplomats in his country. He said that without continued U.S. and international help, “we will not be able to do it.”

Earlier in the day, Clinton acknowledged during her appearance with the Moroccan foreign minister that “it is hard for some people to understand why the United States cannot or does not just prevent” such videos “from ever seeing the light of day.” But she said stopping such expressions was not only “impossible” but also against U.S. values of free expression.

Google, which owns YouTube, said it had acted on its own to stop access to the video in Egypt and Libya. A Google official said the company was “watching carefully” events in other countries.

The administration has criticized other governments for trying to shut down the Internet, bar certain content or jam cellphone and other communications it finds displeasing. It also has assisted dissidents in countries such as Syria in making their voices heard electronically. And it has struggled to develop its own ability to promote U.S. messages through social media. In separate programs, the State Department and the Pentagon have spent tens of millions of dollars to monitor the public communications of others and send out their own.

In a measure of the tension between American diplomats in Cairo and the Egyptian government, a minor tempest broke out Thursday on Twitter between representatives of the Muslim Brotherhood and U.S. Embassy public affairs officials.

The Brotherhood posted a message of support for the embassy staff, saying it was “relieved” that no diplomatic worker had been harmed in the Cairo demonstrations and expressing hope that relations between the countries would be maintained through the “turbulence of Tuesday’s events.”

In response, the U.S. Embassy feed said, “Thanks. By the way, have you checked out your own Arabic feeds? I hope you know we read those too,” an apparent reference to the calls for more protests.

“We understand you’re under a lot of stress,” the Brotherhood replied. “But it will be more helpful if you point out exactly the Arabic feed of concern.”

Birnbaum reported from Cairo. Greg Miller in Washington, Richard Leiby in Kabul and Mohammad al-Qadhi in Sanaa contributed to this report.