SETBACK TO MEDIATION PLAN
The LNA was in control of the former airport, LNA spokesman Ahmed Mismari said, rejecting a claim by the Tripoli interior minister, Fathi Bashagha, that his forces had retaken it.
The LNA said it had lost five soldiers since Thursday.
While the advance has looked fast, so far Haftar's force has mainly crossed sparsely populated areas after taking Gharyan, the last town in the mountains before the road descends to a coastal plain.
In 2014 battles for Tripoli, it took advancing fighters weeks to reach the city centre from the old airport as snipers bogged them down.
Forces from Misrata, a city east of Tripoli, sent more reinforcements to defend Serraj, residents said.
Major ministries are still 20 km away.
Despite their gains, Haftar's forces failed to take a checkpoint about 30 km west of the capital in a bid to close the coastal road to Tunisia. An LNA-allied armed group withdrew overnight from so-called Gate 27, leaving it abandoned in the morning, a Reuters reporter said.
And in another setback, forces allied to Tripoli took 145 LNA fighters prisoner in Zawiya, west of the capital, a western commander, Mohamed Alhudair, told Reuters.
An LNA source confirmed 128 had been captured.
Armed groups allied to the Tripoli government have moved more machinegun-mounted pickup trucks from the coastal city of Misrata to Tripoli to defend it against Haftar's forces.
The offensive is a setback for the United Nations and Western nations trying to mediate between Serraj, 59, who comes from a wealthy business family, and military veteran Haftar.
They met in Abu Dhabi last month to discuss power-sharing.
The United Nations wants to find agreement on a road map for elections to resolve the prolonged instability in Libya, an oil producer and transit point for refugees and migrants trekking across the Sahara with the aim of reaching Europe.
Haftar enjoys the backing of Egypt and the United Arab Emirates, which see him as a bulwark against Islamists and have supported him militarily, according to U.N. reports.
The UAE, however, joined Western countries in expressing its deep concern about the fighting.
Russia said it was not helping Haftar's forces and it supported a negotiated political settlement that ruled out any new bloodshed.
Tunisia has tightened control on its border with Libya in response to the renewed conflict, the defence ministry said.
Former colonial power Italy, which lies across the Mediterranean and has been a destination for migrants, was very worried, Italian Deputy Prime Minister Matteo Salvini said.
"We need to throw water on the fire, not petrol on the fire. I hope that people, acting out of economic or business self-interest, are not looking for a military solution, which would be devastating," Salvini said.