Deputy Minister of the interior Wanis al-Sharif said J Christopher Stevens “was killed along with three other officials”.
The deputy Prime Minister, Mustafa Abu Shagur, later repeated the claim on Twitter.
Mr Stevens, a career officer with the US Foreign Service, had been in the country for less than four months after taking up his post in the capital Tripoli in May.
Fawzi Wanis, who heads the High Security Commission in Benghazi, said Mr Stevens was at the consulate when it was attacked.
An armed mob protesting against a film deemed offensive to Islam attacked the US mission just hours after Islamists also stormed Washington’s embassy in the Egyptian capital Cairo.
The film at the centre of the anti-US protests was made by an Israeli-American who describes Islam as a “cancer” and depicts the Prophet Mohammed sleeping with women.
There has been no comment yet from the US state department.
Following the attack secretary of state Hillary Clinton announced that a state department official had been killed in the Libyan consulate, saying: “We are heartbroken by this terrible loss.”
She added that the US deplored anything that denigrated the religious beliefs of others but that it was no excuse for violence.
Reuters reported that witnesses had seen looters ransacking the consulate in Benghazi and setting off homemade bombs after security forces, who had been trying to hold the gunmen at bay, were forced to withdraw on Tuesday