In a post online, the media office attached to his forces claimed it now had full control of Tripoli international airport and was working to secure the facility.
It posted photos of troops apparently inside the airport, saying “we are standing at the heart of the Tripoli international airport”.
It comes after the UN insisted it is determined to hold a conference on possible elections on time, despite eastern forces in the country advancing on the capital as the conflict continues to escalate.
Libya is governed by rival authorities: the internationally-backed government in Tripoli and the government in the east, which Mr Haftar is aligned to.
Both are backed by an array of militias.
Tripoli airport has not been functional since fighting in 2014 destroyed much of the facility.
Troops also reportedly captured Wadi el Rabeia, south of Tripoli, in clashes with rival militias backing the government of Fayez Sarraj.
Ahmed al Mesmari, a spokesman for the self-styled Libyan National Army (LNA) led by Mr Haftar, said 14 troops had been killed since the offensive was declared.
He claimed rival militias launched four airstrikes on Saturday targeting Mr Haftar’s position in the town of al Aziziya. No casualties were reported.
Mr Haftar declared he was deploying forces to advance on Tripoli on Thursday, sparking fears the conflict could escalate as rival militias from Zawiya and Misrata in the west mobilised to confront his troops.
On Saturday, the UN Security Council called on his forces to halt all military movements and urged all forces in Libya to “de-escalate and halt military activity”.
The LNA offensive escalates a power struggle that has riven Libya since the 2011 overthrow of Muammar Gaddafi.
The UN conference would be staged in the southwestern town of Ghadames on 14-16 April to try to establish elections as a way to end the factional anarchy.
Ghassan Salame, UN special envoy to Libya, said: “We have worked for one year for this national conference, we won’t give up this political work quickly.”
Mr Haftar, 75, is viewed as a new version of former dictator Gaddafi, told al Arabiya TV his offensive would continue until terrorism was defeated.
A former officer in Gaddafi’s army, he enjoys support in Egypt and the UAE, which see him as a buffer against Islamists, according to UN reports.