The UN said the clashes have displaced some 3,400 people, up from an earlier estimate of 2,800
Libya's warring parties Tuesday faced mounting international pressure to halt fighting near the capital that has caused thousands to flee and left several dozen people dead.
UN chief Antonio Guterres called late Monday for a ceasefire in the hostilities, after Tripoli's only functional airport was hit in an air strike.
Guterres "urges the immediate halt of all military operations in order to de-escalate the situation and prevent an all-out conflict," a statement from the United Nations said.
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 recognised by a parallel administration in the east of the country, allied with military commander and strongman Khalifa Haftar.
Haftar's forces, who launched a surprise offensive on the Libyan capital last week, claimed responsibility for Monday's air raid on Mitiga airport. It caused no casualties, but left a metre-deep crater on a runway.
Flights were suspended on Monday, but the airport was due to be reopened to night-time flights only late Tuesday.
The civil aviation authority has decided "only night flights can resume until further notice," the spokesman for Libyan Airlines Mohamad Gniwa told AFP, adding the first flights would be to bring home travellers stuck abroad following the air strike.
Another airport source confirmed the resumption of night-time flights from the former military airbase, without giving further details.
Since his lightning offensive on Tripoli last Thursday, Hafter has defied international calls to halt his advance, including from the UN Security Council and the United States.
The unity government's health ministry on Monday put the death toll in the fighting at 35. Haftar's forces have said 14 of their fighters have died.
The UN said the clashes have 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.
French President Emmanuel Macron spoke with GNA leader Fayez al-Sarraj to voice his "total opposition to the offensive against the capital and the endangering of civilian lives", the unity government said.
The French presidency said in a statement that Macron had also been in contact with Haftar and in his calls expressed his "deep concern about the latest developments", adding it was "imperative" that the fighting ends immediately.
Global powers divided
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 has thrown into sharp relief the divisions between world powers over how to end the chaos that has riven Libya since 2011.
All-party talks led by the UN are due to be held from April 14-16 in the Libyan city of Ghadames.
But despite assurances from UN envoy Ghassan Salame that he remains committed to the conference, there are increasing doubts if it will go ahead as planned.
On one side of the struggle is Haftar, whose key allies are the United Arab Emirates, Egypt and increasingly Saudi Arabia, while he is strongly opposed by their regional foe Qatar as well as Doha's chief supporter Turkey.
Russia has said meanwhile it is not taking sides in the fighting in Libya but behind the scenes, experts say, Moscow is firmly backing Haftar.
"Haftar is ideologically close to Russia," said analyst Alexander Shumilin of the Centre for the Analysis of Middle East Conflicts in Moscow.
"He is supplied with Russian weapons and gladly takes them. He is Moscow's man," he said.
On the other side of the fight, Sarraj's UN-backed government retains substantial support from former colonial power Italy.