President Obama: "There is absolutely no justification for this type of senseless violence".
The attack in Libya that killed the US ambassador and several other people was complex and professional, amid reports the perpetrators may have had links to jihadist groups.
The assault had earlier been thought to have been a spontaneous reaction to protests over an anti-Islamic film.
There were also clashes outside the US embassy in Cairo on Thursday.
Thousands of people gathered outside the building in the Egyptian capital for a second night, chanting and starting fires. Police and troops fired tear gas to break up the crowds, some of whom were seen carrying petrol bombs.
On Wednesday, demonstrators in Cairo angry at the film - called Innocence of Muslims - had breached the walls of the US embassy and torn down the flag.
Armed men stormed the consulate in the city of Benghazi on Tuesday night.
It is believed Ambassador J Christopher Stevens died of smoke inhalation. Three other Americans and up to 10 Libyans also died in the attack.
On Wednesday, President Barack Obama vowed to bring to justice those behind the attack, but said the US would not "break bonds" with the new Libyan government.
A senior US official quoted by AFP news agency said the Benghazi attackers appeared to have used the demonstrations as a pretext to staging an assault.
"This was a complex attack," he told the news agency. "They seemed to have used this (protest) as an opportunity."
US officials told Reuters news agency there were suspicions that a militia known as the Ansar al-Sharia brigade was responsible, although the group has denied the claim.
They said there were also reports that al-Qaeda's north Africa-based affiliate, al-Qaeda in the Islamic Maghreb, may have been involved, the news agency reports.
Libyan and US security forces tried to retake the compound several times, US officials said, but only succeeded early on Wednesday.
One of the Americans killed was Sean Smith, a US State Department employee. The other victims were not identified.
Seventeen-year-old Hamam, who took part in the attack, said that Ansar al-Sharia cars had arrived at the start of the protest but later left.
"The protesters were running around the compound just looking for Americans, they just wanted to find an American so they could catch one," he said.
"We started shooting at them, and then some other people also threw hand-made bombs over the fences and started the fires in the buildings.
Little is known about the origins of the film, including about a man named as Sam Bacile, reported as being behind its production.
BBC reporters probing his background on Wednesday were unable to confirm personal details.
Egypt's Coptic Church has issued a statement condemning the production, after reports that some Copts in the US had financed the film.