UN Secretary-General Antonio Guterres on Monday called for an immediate halt to fighting in Libya, after Field Marshal Khalifa Haftar's forces launched an air strike on Tripoli's only functioning airport.
The UN said thousands have fled the capital since the Libya National Army launched an assault last week which has killed dozens of people.
Mr Guterres wants the assault to be brought to an end "to prevent an all-out conflict," the UN said on Monday.
It said the Secretary-General "strongly condemns the military escalation and ongoing fighting in and around Tripoli, including the attack by a Libyan National Army aircraft against Mitiga airport".
There have been violent power struggles between an array of armed groups in Libya since dictator Muammar Qaddafi was overthrown in 2011.
The UN-backed Government of National Accord controls Tripoli, but its authority is not recognised by a parallel administration in the east of the country, backed by Field Marshal Haftar.
He has defied international calls to halt his advance on the capital, including pressure from the UN Security Council and the US.
"I make a very strong appeal to Libyan leaders, and in particular to Field Marshal Haftar, to stop all military activities and to return to the negotiating table," the EU's foreign policy chief Federica Mogherini said after talks with foreign ministers.
The GNA said its leader Fayez Al Sarraj spoke on the phone with French President Emmanuel Macron, who stated his strong opposition to the assault on Tripoli. The French presidency confirmed the call took place, without confirming details of the discussion.
LNA spokesman Ahmad Al Mesmari said Monday's air strike on Mitiga airport, to the east of the capital, targeted a MiG-23 military plane and a helicopter. A security source at the airport said no one was injured in the attack.
"This attack constitutes a serious violation of international humanitarian law, which prohibits attacks against civilian infrastructure," the UN's envoy to Libya, Ghassan Salame, said.
A spokesman for Libyan Airlines said the civil aviation authority suspended aerial traffic until further notice.
Field Marshal Haftar served as a military chief under Qaddafi and has become a major player in the country's political struggle.
Field Marshal Haftar seized control of much of eastern Libya and won battles in the south of the country, before turning his sights to Tripoli, where he wants to remove "terrorists and mercenaries" from the city.
His assault threatens to derail diplomatic efforts to find a political solution to the conflict.
On Sunday, Field Marshal Haftar's fighters clashed with other armed western Libyan groups. Forces backing the GNA then announced a counteroffensive, known as "Volcano of Anger".
After a pause, fighting resumed on Monday around a destroyed airport about 30 kilometres south of Tripoli, and the rural area of Wadi Rabi further east.
The US has appealed for the fighting to stop, a call that was echoed by the UN Security Council.
Russia, a key supporter of Field Marshal Haftar, alongside the UAE and Egypt, blocked the council from adopting a formal statement against the LNA on Sunday.
The Kremlin has since called on "all sides to reject actions that could provoke bloodshed in battle and the deaths of civilians".
On Monday, the unity government's health ministry said 35 people have been killed in the fighting, and the LNA said 14 of their fighters were dead.
The UN said the fighting has also displaced about 3,400 people.
"Clashes with heavy weapons are affecting residential areas, and an unknown number of civilians are unable to flee these locations," UN spokesman Stephane Dujarric said in New York on Monday. "We have no positive news to report on our call for a humanitarian truce."
Field Marshal Haftar launched his offensive days before a UN conference aimed at uniting Libya's rivals and paving the way for elections to take place.
Mr Salame has insisted the international community is determined to hold the conference on April 14-16.
The UN mission in Libya said on Twitter that Mr Salame met Mr Al Sarraj in Tripoli on Monday to discuss how to assist the GNA.