Libyan military strongman Khalifa Haftar pushed on with his assault on Tripoli Monday, defying international calls for a ceasefire days into a battle that has left dozens dead.

Oil-rich Libya has been rocked by violent power struggles between an array of armed groups since the NATO-backed overthrow of dictator Moamer Kadhafi in 2011.

Haftar, a former Kadhafi military chief, has emerged as a major player, his self-styled Libyan National Army backing an administration in the country's east in opposition to the UN-backed unity government based in Tripoli.

Having seized control of much of eastern Libya and buoyed by a series of victories in the desert south, Haftar turned his sights on Tripoli this month, vowing to "cleanse" it of "terrorists and mercenaries".

After a pause overnight, fighting resumed Monday morning around the capital's destroyed airport, some 30 kilometres south of Tripoli, and the rural area of Wadi Rabi further east.

World powers have expressed alarm at the violence, saying it threatens to further destabilise Libya and derail UN-led efforts to find a political solution to the country's woes.

The US has appealed for an "immediate halt" to combat operations and the UN Security Council has called on Haftar's forces to halt their advance.

On Sunday Russia blocked proposals for the council to adopt a formal statement, instead insisting that all Libyan forces be urged to stop fighting, diplomats said.

Moscow is a key supporter of Haftar, along with Egypt and the United Arab Emirates.

But the Kremlin on Monday urged "all sides to reject actions that could provoke bloodshed in battle and the deaths of civilians".

Fierce clashes Sunday near Tripoli saw Haftar's fighters and an array of powerful western Libyan armed groups exchanging fire including air strikes.

Forces backing the Tripoli-based Government of National Accord on Sunday announced a counteroffensive named "Volcano of Anger".

Spokesman Colonel Mohamed Gnounou said it was aimed at "purging all Libyan cities of aggressor and illegitimate forces", in reference to Haftar's fighters.

Unity government health minister A'hmid Omar told Libya's Al-Ahrar television station late Sunday that around 50 people had been wounded along with those killed.

His ministry on Monday put the death toll at 35.

Haftar's forces have said 14 of their fighters have died. The UN Humanitarian Coordinator in Libya, Maria Ribeiro, said Monday the fighting had displaced more than 2,800 people, blocked rescuers from reaching casualties and damaged electricity lines.

She again urged the warring parties to implement a temporary humanitarian ceasefire.

The previous day, fighting raged throughout a two-hour window set by the UN for a pause in hostilities for civilians and the wounded to flee.

Haftar's offensive has threatened to plunge the country into a full-blown civil war and once again thwart diplomatic efforts to find a solution to Libya's woes.

It was launched just days ahead of a planned UN conference aimed at uniting Libya's rivals and paving the way for elections.

Envoy Ghassan Salame has insisted the UN was "determined" to go ahead with the April 14-16 conference.

The UN mission in Libya said on Twitter that Salame met Monday with unity government head Fayez al-Serraj in Tripoli to discuss how to "assist at this critical and difficult juncture".

(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)