* U.S. embassy in Yemen stormed, scuffles at Egypt embassy
* Violence follows killing of U.S. ambassador in Libya
* Libya says arrests four in investigation of attack
* U.S. sending two Navy destroyers toward Libya
By Mohammed Ghobari and Edmund Blair
SANAA/CAIRO, Sept 13 (Reuters) - Demonstrators attacked the U.S. embassies in Yemen and Egypt on Thursday in protest at a film they consider blasphemous to Islam, and American warships headed towards Libya after the U.S. ambassador there 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.
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 Qaeda-linked group.
U.S. Secretary of State Hillary Clinton said Washington had nothing to do with the crudely made film posted on the Internet, which she called "disgusting and reprehensible."
The amateurish production, entitled the "Innocence of Muslims," and originating in the United States, portrays Mohammad as a womaniser, a homosexual and a child abuser.
For many Muslims, any depiction of the Prophet is blasphemous and caricatures or other characterisations have in the past provoked violent protests across the Muslim world.
Demonstrations spread further on Thursday, with U.S. embassies again the targets of popular anger among Muslims questioning why the United States has failed to take action against the makers of the film.
Hundreds of Yemenis broke through the main gate of the heavily fortified U.S. embassy compound in the capital 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 central Cairo after climbing into the embassy compound and tearing down the American flag. The state news agency said 13 people were hurt in violence which erupted late on Wednesday, following initial protests on Tuesday.
Around 200 demonstrators gathered outside the U.S. embassy in Kuwait shouting slogans such as "God is great." They hoisted banners, one of which bread in English: "USA stop the bullshit. Respect us."
Kuwaiti riot police encircled the crowd of men protesting peacefully in their traditional Kuwaiti dress.
On Thursday, the U.S. consulate in Berlin was partially evacuated after an employee fell ill on opening a suspicious envelope. Bangladeshi Islamists tried to march on the U.S. embassy in Dhaka and Iranian students protested in Tehran.
Earlier in the week, there were protests outside U.S. missions in Tunisia, Morocco and Sudan.
The U.S. ambassador to Libya was killed during a protest against the film on Tuesday at the U.S. consulate in the eastern Libyan city of Benghazi when Islamists armed with guns, mortars and grenades staged military-style assaults on the mission and a safe house refuge.
A Libyan doctor at a Benghazi hospital 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 U.S. troops sent by helicopter from Tripoli to rescue diplomats from the safe house came under mortar attack.
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.
Tuesday's incident, on what was the 11th anniversary of al Qaeda's attacks on the United States on Sept. 11, 2001, has created an unwanted foreign policy crisis for Obama ahead of his bid for reelection in November.
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 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 first ship, 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, speaking on condition of anonymity.
"We don't know if they are affiliated with a particular group or not, there are a lot of suspicions but the we have to go through with the investigation and find out who these people are and if they belong to a particular group, then we have to deal with that group."
The U.S. military also dispatched a Marine Corps anti-terrorist team to boost security in Libya, whose leader Muammar Gaddafi was ousted in a U.S.-backed uprising last year.
Republican Mitt Romney, Obama's challenger, criticised the government's response to the crisis earlier this week, saying it was disgraceful to be seen to be apologising for American values of free speech.
Obama's campaign accused Romney of trying to score political points at a time of national tragedy and the challenger also provoked some criticism from within his own party.
Campaigning on 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.
Obama's administration again sought to calm Muslim tensions on Thursday.
Clinton said Washington rejected the film's message absolutely, and added: "It appears to have a deeply cynical purpose: to denigrate a great religion and provoke rage."
At the same time, Clinton noted the history of religious tolerance in the United States and its commitment to freedom of speech and said there was no justification for people to respond with violence.
"I know it is hard for some people to understand why the United States cannot or does not just prevent these kinds of reprehensible videos from ever seeing the light of day," she said. "I would note that in today's world, with today's technologies, that is virtually impossible.
"But even if it were possible our country does have a long tradition of free expression which is enshrined in our constitution and our law. And we do not stop individual citizens from expressing their views no matter how distasteful they may be," she added.
Among the assailants in Benghazi, Libyans identified units of a heavily armed local Islamist group, Ansar al-Sharia, which sympathises with al Qaeda and derides Libya's U.S.-backed bid for democracy.
Former Libya militant commander Noman Benotman, now president of Britain's Quilliam think tank, said Western officials were investigating a possible link with a paramilitary training camp about 100 miles (160 km) south of the eastern Libyan town of Derna, near the Egyptian border.
U.S. officials said there were suggestions members of al Qaeda's North Africa-based affiliate may have been involved.
Libya's new Prime Minister Mustafa Abu Shagour confirmed arrests had been made in the investigation into the attack and more could be expected.
"We don't know if they are affiliated with a particular group or not, there are a lot of suspicions but ... we have to go through with the investigation and find out who these people are and if they belong to a particular group, then we have to deal with that group."
"We ... assure the people that we are going after them, that we are going to bring them to justice and they have to be punished for their act. This is not acceptable.
A spokesman for Ansar al-Sharia denied it had played a role in the attack on the U.S. consulate and blamed the violence on firing on the protesters by consulate staff.
"It was a peaceful protest, and the firing on the protesters inflamed the situation and gave it a different course," Hani Mansouri told a news conference in Benghazi.
At the same time, Mansouri said the United States should have had the wisdom to evacuate its ambassador on the Sept. 11 anniversary as a precaution.
Yemen, a key U.S. ally, is home to Al Qaeda in the Arabian Peninsula (AQAP), viewed by Washington as the most dangerous branch of the militant network established by Osama bin Laden.
Clashes near the U.S. embassy there flared up on and off but died down as night fell. Residents living nearby said they feared more violent protests after Friday prayers.
"It is a dangerous situation," one resident told Reuters. "I cannot wait until the morning to move my family to another neighbourhood until the situation is totally calm."
In Nigeria, the government put police on high alert and stepped up security around all foreign missions, also fearing an Islamist backlash, possibly after Friday prayers.
An actress in the California production that has provoked the unrest said the video as it appeared bore no resemblance to the original filming. She said she had not been aware it was about the Prophet Mohammad.
Many Muslim states focused their condemnation on the film and will be concerned about preventing a repeat of the fallout seen after publication in a Danish newspaper of cartoons of the Prophet Mohammad. This touched off riots in the Middle East, Africa and Asia in 2006 in which at least 50 people were killed.
Afghan President Hamid Karzai has called the making of the movie a "devilish act" but said he was certain those involved in its production were a very small minority.
The U.S. embassy in Kabul has appealed to Afghan leaders for help in "maintaining calm" and Afghanistan ordered the YouTube site shut down so Afghans would not be able to see the film. YouTube, owned by Google Inc, said it would not remove the clip but had blocked access in Egypt and Libya.
Libyan leader Mohammed Magarief and Yemeni President Mansour Hadi both apologised to the United States over the attacks and Egypt's Islamist President Mohamed Mursi condemned them on television while also rejecting any "insult to the Prophet".
Russian President Vladimir Putin, a sharp critic of last year's Western military intervention in Libya and of Western backing for Syria's rebels, called Stevens' death a tragedy and said he believed Western support for rebels in Arab countries was causing chaos.