SANAA/CAIRO — Demonstrators attacked the U.S. embassies in Yemen and Egypt Thursday in protest of a film they consider blasphemous to Islam, and the United States sent war ships toward Libya, where the U.S. ambassador was killed in related violence this week.

In Libya, authorities said they had made four arrests in the investigation into the attack that killed ambassador Christopher Stevens and three other Americas in Benghazi on Tuesday. (See more, Page A5.)

President Barack Obama has vowed to bring to justice those responsible for the Benghazi attack, which U.S. officials said may have been planned in advance — possibly by an al Qaida-linked group.

Secretary of State Hillary Clinton said Washington had nothing to do with the crudely made “Innocence of Muslims” film posted on the Internet, which she called “disgusting and reprehensible.”

Hundreds of Yemenis broke through the main gate of the heavily fortified U.S. embassy compound in Sanaa, shouting “We sacrifice ourselves for you, Messenger of God.” They smashed windows of security offices outside the embassy and burned cars.

A security source said at least 15 people were wounded, some by gunfire, before the government ringed the area with troops.

In Egypt, protesters hurled stones at a police cordon around the U.S. embassy in Cairo after climbing into the compound and tearing down the American flag. The state news agency said 13 people had been hurt in violence since late on Wednesday.

Around 200 demonstrators gathered outside the U.S. embassy in Kuwait and hoisted banners.

In Bangladesh, Islamists tried to march on the U.S. embassy in Dhaka and Iranian students protested in Tehran.

The U.S. ambassador to Libya was killed during a protest against the film when Islamists armed with guns, mortars and grenades staged military-style assaults on the Benghazi mission.

A Libyan doctor said Stevens died of smoke inhalation. U.S. information technology specialist Sean Smith also died at the consulate, while two other Americans were killed when a squad of security personnel sent by helicopter from Tripoli to rescue diplomats from a safe house came under mortar attack.

Of the latter, one was identified by his family as Glen Doherty, 42, a former Navy SEAL who worked as a private security contractor. The other was identified as former navy SEAL, Tyrone Woods, 41.

In an interview with the U.S. network ABC News last month, Doherty said he was working with the State Department to round up and destroy shoulder-fired surface-to-air missiles that fell into the hands of militants after Moammar Gadhafi’s overthrow.

Stevens, 52, had spent a career operating in perilous places, mostly in the Arab world, and became the first American ambassador killed in an attack since Adolph Dubs, the U.S. envoy to Afghanistan, died in a 1979 kidnapping attempt.

Speaking at a campaign rally in Colorado on Thursday, Obama said he had ordered his administration to do whatever was necessary to protect Americans abroad and that aides had been in contact with other governments “to let them know they’ve got a responsibility to protect our citizens.”

The U.S. military has dispatched two destroyers toward the Libyan coast, in what an official said was a move to give the administration flexibility for any future action. The USS Laboon, was already in position and the other destroyer, the USS McFaul, was at least a day away, a U.S. official said.

The U.S. military also sent a Marine Corps anti-terrorist team to boost security in Libya.

Republican Mitt Romney, Obama’s challenger, criticized the President’s response to the crisis earlier this week, saying it was disgraceful to be seen to be apologizing for American values of free speech.

Campaigning Thursday, Romney stopped short of repeating the charge, but said that under Obama the United States seemed to be at the mercy of world events rather than shaping them, and argued for a stronger military, at a time when U.S. armed forces are facing an unprecedented budget squeeze.