A "big advance" has been made in the probe into the deadly attack on the US consulate in Libya's second city Benghazi, Prime Minister Mustafa Abu Shagur said today.

In his first interview since his election as premier last night, Abu Shagur said that arrests had already been made and that more were under way.

"We have made a big advance. We have some names and some photographs," he said. "Arrests have been made and more are under way as we speak."

The new prime minister did not elaborate on how many suspects were in custody or what groups, if any, they were connected to. "We don't want to categorise these people until we know all the facts," he said.

Deputy Interior Minister Wanis al-Sharif was similarly reticent about going into details when he spoke to AFP earlier the same day.

"The interior and justice ministries have begun their investigations and evidence gathering and some people have been arrested," he said.

He declined to give any details of the number of people in custody or their backgrounds "so as not to hamper the smooth running of the investigation."

Initial reports said that Ambassador Chris Stevens and three other Americans were killed by a mob outside the consulate in Benghazi on Tuesday as they tried to flee an angry protest against a US-produced movie deemed offensive to Islam.

But it is now believed Stevens died from smoke inhalation after becoming trapped in the compound when suspected Islamic militants fired on the building with rocket-propelled grenades and set it ablaze.

The finger of blame initially fell on hardline Sunni

Islamists of the Salafist group Katibat Ansar al-Sharia (Brigade of the Supporters of Sharia).

But in a statement today, the group condemned "the accusations without any verification or investigation" which had emerged against it in the Libyan media.

In Benghazi, journalists managed to enter the residential complex that housed the US consulate and described a scene from a warzone.

Blood stained the ground at the main entrance of the consulate, which is part of a three-building compound, an AFP photographer said.

All the buildings were blackened by fire, furniture destroyed and walls punctured by bullets, said photographer who managed to enter the grounds with other journalists after obtaining permission from the owner of the compound.

Security officers and police were nowhere to be seen, inside or outside the consulate, with no sign of an investigation.

A spokesman for the interior ministry's security commission told AFP the inquiry will be "very complicated" because the crowd outside the consulate had been very mixed.

"There were extremists, ordinary citizens, women, children and criminals," Abdelmonem al-Horr said. "There were also shots fired from a nearby farm. We need time to determine who was responsible."

US President Barack Obama discussed the attack by phone with Mohamed al-Megaryef, president of Libya's highest political authority, the General National Congress, and Megaryef offered Libya's apologies for the attack.