Thousands have fled violence in the capital city, according to the United Nations, since Haftar launched a surprise assault last week which has left dozens dead.

Secretary-General Guterres "urges the immediate halt of all military operations in order to de-escalate the situation and prevent an all-out conflict," said a UN statement late Monday.

He "strongly condemns the military escalation and ongoing fighting in and around Tripoli, including the aerial attack today by a Libyan National Army (LNA) aircraft against Mitiga airport."

The oil-rich northern African country has been rocked by violent power struggles between an array of armed groups since the NATO-backed overthrow of dictator Moamer Kadhafi in 2011.

The UN-backed Government of National Accord (GNA) controls the capital, but its authority is not recognized by a parallel administration in the east of the country, backed by Haftar.

The strongman has defied international calls to halt his advance on Tripoli, including from the UN Security Council and the United States.

"I make a very strong appeal to Libyan leaders and in particular to Haftar to stop all military activities... and to return to the negotiation table", the EU's foreign policy chief Federica Mogherini said after talks with EU foreign ministers.

The GNA said French President Emmanuel Macron spoke with its leader Fayez al-Sarraj of his "total opposition to the offensive against the capital and the endangering of civilian lives".

The French presidency confirmed the call took place, without releasing details of the discussion.

Ahmad al-Mesmari, a spokesman for Haftar's self-styled Libyan National Army, claimed Monday's air strike against Mitiga airport, east of the capital which targeted a MiG-23 military plane and a helicopter.

A security source at the airport said the strike hit a runway without causing casualties.

"This attack constitutes a serious violation of international humanitarian law which prohibits attacks against civilian infrastructure," said the UN's envoy to Libya, Ghassan Salame.

A spokesman for national carrier Libyan Airlines said the civil aviation authority decided "to suspend aerial traffic until further notice".

An airport source, who did want to be named, confirmed the suspension.

- 'Immediate halt' -

Haftar is a former Kadhafi military chief who has emerged as a major player in Libya's political struggle.

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

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

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

Forces backing the GNA then announced a counteroffensive dubbed "Volcano of Anger".

After a pause, fighting resumed Monday around the capital's destroyed main airport, some 30 kilometres (18 miles) south of Tripoli, and the rural area of Wadi Rabi further east.

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

On Sunday Russia, a key supporter of Haftar, along with Egypt and the United Arab Emirates, blocked the council from adopting a formal statement against the strongman.

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

- Civil war fears -

The unity government's health ministry on Monday put the death toll at 35. Haftar's forces have said 14 of their fighters have died.

The UN said the fighting has displaced some 3,400 people, up from an earlier estimate of 2,800.

"Clashes with heavy weapons are affecting residential areas, and an unknown number of civilians are unable to flee these locations," UN spokesman Stephane Dujarric told reporters in New York on Monday.

"We have no positive news to report on our call for a humanitarian truce."

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

The UN's Salame has insisted the international community is "determined" to go ahead with the April 14-16 conference.

The UN mission in Libya said on Twitter that Salame met Monday with Sarraj in Tripoli to discuss how to "assist at this critical and difficult juncture".