Rival militia clashed for a fourth day on the outskirts of the Libyan capital in the deadliest and most sustained violence since the death of Muammar Gaddafi.

Fighters attacked each other late on Sunday, November 13, with rockets, mortars and machine guns.

The fighting, in which at least 13 people were killed since late last week, raised concerns about the ability of Libya's transitional government to disarm thousands of gunmen and restore order after the eight-month civil war.

Libya's interim leader, Mustafa Abdul Jalil, said his National Transitional Council brought together elders from the feuding areas - the city of Zawiya and the nearby tribal lands of Warshefana - over the weekend and that the dispute had been resolved.

"I want to assure the Libyan people that everything is under control," he said.

But fighting continued as he spoke. Heavy gunfire and explosions from rocket-propelled grenades were heard for hours on Sunday in the area between the Warshefana lands, about 30 kilometres west of Tripoli, and in Zawiya, another 15km to the west.

At one stage the two sides were battling for control of a major military camp of the removed regime, said a fighter from Tripoli.

The camp, once a base of elite forces commanded by one of Qaddafi's sons, Khamis, is located on a motorway midway between Tripoli and Zawiya.

At least 13 people were killed in the fighting, including four from Zawiya and nine from Warshefana, according to gunmen and a hospital doctor in Warshefana, The Associated Press reported.