As violent anti-American protests spread to Yemen on Thursday, U.S. President Barack Obama said the U.S. "would not consider Egypt an ally, but we would not consider them an enemy."

In his first interview since the murder of U.S. Ambassador Chris Stevens by a mob in Benghazi, Libya, on Tuesday night, as well as the violent protests outside the American Embassy in Egypt, Obama told the Spanish-language TV network Telemundo: “We are going to have to see how they respond to this incident, how they respond to, for example, maintaining the peace treaty with Israel. So far, at least, what we've seen is, in some cases, that they've said the right things and taken the right steps; in others, how they've responded to various events may not be aligned with our interests, and so I think it's still a work in progress."

Protests continued outside the American Embassy in Cairo early Thursday morning. The violent protests over an anti-Islam film purportedly made by an American, spread to Yemen on Thursday, with hundreds of demonstrators storming the U.S. Embassy in Sanaa. Security guards tried to hold them off by firing into the air, witnesses said.

They said the demonstrators smashed windows of the security offices outside the embassy before breaking through the main gate of the heavily fortified compound in eastern Sanaa. Yemeni security forces who rushed to the scene fired in the air and used tear gas to disperse the demonstrators and were eventually able to drive them out of the compound. It was not immediately clear whether anyone was inside the embassy at the time of the attack.

Film on Al-Jazeera television showed demonstrators jumping up and down on the parapet of the building and scaling the walls. Young demonstrators shouting, "We redeem, Messenger of God," smashed windows of the security offices outside the embassy with stones and burned cars before breaking through the main gate of the compound. Others held aloft banners declaring “Allah is Greatest.”

The Yemeni Embassy in Washington condemned the attack and vowed to ensure the safety of foreign diplomats and to step up security measures around their missions in the country. They also said that no casualties had been reported in the incident.

On Wednesday, Obama dispatched two naval destroyers and 50 Marines to Libya and also ordered increased security at American missions around the world.

Obama also called the presidents of Libya and Egypt to urge them to continue working with the U.S. to ensure the safety of diplomatic personnel.

He thanked Libyan President Mohamed Magariaf for his condolences over the deaths of U.S. Ambassador Chris Stevens and three other State Department officers during an assault on the U.S. Consulate in Benghazi Tuesday. The U.S. State Department said it appeared that Stevens' security detail lost the ambassador in the burning consulate, and did not locate him again until his body was delivered to U.S. personnel at the Benghazi airport.

The White House says the two leaders agreed to work together to bring the attackers to justice.

Egyptian President Mohammed Morsi promised Egypt "would honor its obligation to ensure the safety of American personnel," the White House said. Obama told Morsi that while "he rejects efforts to denigrate Islam ... there is never any justification for violence against innocents."

In a televised address on Thursday, Mosri said he supported peaceful protests, and that it was wrong to attack people or embassies.

"Expressing opinion, freedom to protest and announcing positions is guaranteed, but without assaulting private or public property, diplomatic missions or embassies," he said.

• The end of US naivete? by Eyal Zisser

• Another link in the violent chain reaction, by Dan Margalit