By BBCPresident Barack Obama has vowed to bring to justice the killers of the US ambassador to Libya during protests against a film that mocks Islam.
But he told reporters that the attack on the American consulate in Benghazi would not break the bonds between the US and the new Libyan government.
Mr Mitt Romney, President Obama‘s political foe, criticised the handling of the crisis.
Ambassador J Christopher Stevens reportedly died of smoke inhalation after a crowd stormed the consulate.
Three other Americans were also killed, amid reports that rocket-propelled grenades had been fired during the assault on Tuesday night.
The consulate was set ablaze and a charred car could be seen parked near the damaged buildings on Wednesday.
A US marine anti-terrorism team is being sent to Libya to bolster security after the attack, a US Defence source told reporters in Washington.
Protesters against the film also attacked the US embassy in Cairo on Tuesday night.
Speaking in the Rose Garden at the White House, President Obama told reporters: “Make no mistake. Justice will be done.”
He said he condemned “in the strongest possible terms the outrageous and shocking” attack.
Washington will want answers from the Libyan government about the scale of the security measures in place at its consulate in Benghazi and how demonstrators were able to get into the building.
More broadly the ambassador’s death highlights the continuing instability in Libya as the country struggles to establish security and the rule of law.
The country is awash with weapons and armed militias – some of a salafist or extreme Islamic fundamentalist outlook – hold sway in many areas.
Libya’s interim leader Mohammed Magarief, apologised to the US over the killings, which he called “cowardly criminal acts”.
Reports say a militia known as the Ansar al-Sharia brigade was involved in the attack, but the group has denied the claim, the BBC’s Rana Jawad in Tripoli says.
Mr Stevens and his staff went to the consulate in an attempt to evacuate the site after it was attacked, the Associated Press news agency said.
The building apparently came under attack by a crowd armed with guns and rocket-propelled grenades.