Fighting raged south of Libya's capital today despite a UN call for a two-hour ceasefire, as forces of strongman Khalifa Haftar and the internationally recognised government exchanged air strikes.

The unity government said the fighting had killed 21 people, while the United Nations said there had been "no truce" despite calls for a two-hour pause in fighting for civilians and the wounded to flee.

Oil-rich Libya has been riven by chaos since the NATO-backed uprising in 2011 that killed dictator Muammar Gaddafi, as rival administrations and armed groups have battled for power.

Mr Haftar's offensive on Tripoli, launched on Thursday, has threatened to plunge the country into a full-blown civil war and once again derail tentative diplomatic efforts to find a political solution to Libya's woes.

After a pause overnight, fierce fighting flared this morning south of Tripoli between Mr Haftar's self-styled Libyan National Army (LNA) and forces backing the internationally recognised Government of National Accord (GNA).

As clashes raged in the rural area of Wadi Raba and the destroyed international airport south of the capital, a spokesman for pro-GNA forces announced a counter-offensive.

Colonel Mohamed Gnounou told reporters that operation "Volcano of Anger" is aimed at "purging all Libyan cities of aggressor and illegitimate forces", in reference to Mr Haftar's fighters.

The LNA said it had carried out its first air raid on a Tripoli suburb, defying international calls for a ceasefire.

The unity government's health ministry said today at least 21 people had been killed and 27 wounded since the fighting began, without specifying whether civilians were among the dead.

Mr Haftar's force said yesterday that 14 of its personnel had been killed, while the Libyan Red Crescent reported the death of one of its doctors.

Emergency services spokesman Oussama Ali said rescuers "have not been able to enter" the battle zones.