Washington has deployed two U.S. Navy destroyers and 50 Marines to Libya in response to the killing of the U.S. ambassador in Benghazi.
The troops have been dispatched to provide security at the main U.S. Embassy in the capital, Tripoli, where staff numbers are being cut to emergency levels. Staff also were being evacuated from the U.S. diplomatic mission in Benghazi.
U.S. officials were quoted as saying the military was moving two U.S. destroyers toward the Libyan coast "as a precautionary measure."
"The United States condemns, in the strongest terms, this outrageous and shocking attack," Obama said. "We are working with the government of Libya to secure our diplomats. I've also directed my administration to increase our security at diplomatic posts around the world. And make no mistake -- we will work with the Libyan government to bring to justice the killers who attacked our people."
Obama has called the leaders of Egypt and Libya to discuss security cooperation.
The U.S. Embassy in Cairo also was stormed late on September 11 by a crowd of Muslim protesters said to be angry about a film privately produced in the United States that insults the Prophet Muhammad.
Initial reports said Ambassador Christopher Stevens and three other Americans were killed by a mob in eastern Libya that was angry about the same film.
But Washington was reportedly investigating whether the assault was a plot by Al-Qaeda affiliates or sympathizers who used the protests as a diversion for a coordinated attack on the anniversary of the September 11, 2001, terrorist attacks in the United States.
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U.S. officials say they already have unmanned drone aircraft at their disposal to help track militants who may have carried out the Benghazi attack.
The violence was seen by some as a possible threat to international cooperation to establish a stable Libyan government following the overthrow one year ago of Muammar Qaddafi by Libyan forces with NATO air support.
After the rebel victory in Libya, in prepared remarks for his confirmation hearing in the U.S. Senate in March 2012, Stevens wrote optimistically about the rebels and the potential for the United States to help.
Russian Foreign Minister Sergei Lavrov said he was "shocked by the tragic deaths" of the U.S. diplomats. In a telegram to his U.S. counterpart, Hillary Clinton, he said the attack "once again affirms the need for joint efforts of our countries and the entire world community in the fight against the evil of terrorism in all its forms."
Leaders from Afghanistan and Egypt were among others to have condemned the Benghazi violence.
PHOTO GALLERY: Flames engulf the U.S. Consulate in eastern Libya late on September 11, and its aftermath the following day:
New Libyan PM Chosen
Vehicles are engulfed in flames after they were set on fire inside the U.S. Consulate compound.
A gunman reacts as the U.S. Consulate compound in Benghazi burns behind him.
A car burns inside the U.S. Consulate compound.
A vehicle and surrounding buildings burn after they were set on fire at the U.S. Consulate compound.
Libya's National Transitional Council chairman Mustafa Abdel Jalil (right) meets with U.S. Ambassador to Libya Chris Stevens (left) in Tripoli on June 7. Stevens was killed in the violence.
The U.S. Consulate in Benghazi burns.
A burned-out vehicle smolders inside the U.S. Consulate compound.
A burned house and car are seen inside the U.S. Consulate compound.
A man stands inside the U.S. Consulate, which was attacked and set on fire by gunmen.
The head of Libya's national assembly, Mohammed Magarief, pledged that the authorities would bring the perpetrators to justice.
The incident came on the eve of a vote by the Libyan National Assembly to elect a prime minister.
In the shadow of the Benghazi violence, lawmakers on September 12 chose Deputy Prime Minister Mustafa Abu Shagur to head the next government.
Shagur narrowly beat Mahmoud Jibril, who served as interim prime minister following the uprising against Qaddafi last year, in a runoff vote.
Shagur has pledged to make security a priority during his 18-month tenure. Shagur has a long history of opposition to Qaddafi. He earned a doctorate in the United States and worked as an academic and optical engineer.
More Anger Over Film
Meanwhile in Egypt, protesters have clashed with security forces after crowds returned to the U.S. Embassy in Cairo for a second evening of demonstrations over the film.
Reports said police fired tear gas at the demonstrators, some of whom were seen carrying Molotov cocktails.
Although the 14-minute video for the anti-Islamic film
, "Innocence of Muslims," was posted on YouTube months ago, fierce protests were sparked after an Egyptian cleric dubbed the clip into Arabic in early September.
With reporting by Reuters, AP, AFP, dpa, and "The Guardian"