The UN said the clashes have displaced some 3,400 people
The United Nations on Tuesday postponed a Libyan national conference aimed at drawing up an election roadmap because of fighting raging near the capital, in another setback to peace efforts.
The move came as the North African country's warring parties faced mounting international pressure to halt violence that has caused thousands to flee and left several dozen people dead.
"We cannot ask people to take part in the conference during gunfire and air strikes," UN envoy Ghassan Salame said.
He expressed hope that the meeting, which had been scheduled for next week, would take place "as soon as possible".
UN chief Antonio Guterres called for an "immediate halt" to hostilities, after Tripoli's only functional airport was hit in an air strike on Monday by the forces of strongman Khalifa Haftar.
After a night-time lull, fighting resumed on Tuesday morning south of the city, a security source said.
The oil-rich 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 Haftar.
The strongman'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.
Salame said the attack "constitutes a serious violation of international humanitarian law which prohibits attacks against civilian infrastructure".
Flights were suspended on Monday, but the airport was due to be reopened to night-time flights only late Tuesday.
Since launching his lightning offensive on Tripoli last Thursday, Hafter has defied international calls to halt the 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.
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.
International efforts to end the Libyan conflict have repeatedly failed.
Rival leaders agreed last year to hold elections before December 10, 2018 under a French plan, but that vote never materialised.
The national conference, which had been scheduled for April 14-16 in the central city of Ghadames, aimed to fix dates for legislative and presidential elections, and work towards a new constitution.
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.
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.