An airstrike hit a building near a feedstock plant, but a member of the LNA said the force had targeted a military position.
The UN-backed GNA said on Facebook that drones operated by the United Arab Emirates carried out the airstrikes against the positions of a force allied to it.
The UAE is one of Haftar's foreign backers, providing him with weapons and funds.
Mitiga, the Libyan capital's only functioning airport, was also struck in the early hours of Monday, according to an LNA source. The airport has been closed due to continued air strikes.
Haftar ordered militia groups loyal to him to invade Tripoli in an unsuccessful attempt to seize it on April 4. Almost five months after launching the offensive, Haftar's forces remain locked in a stalemate against the GNA on Tripoli's southern outskirts.
According to the latest figures by the World Health Organization (WHO), the fighting around Tripoli has killed at least 1,093 people and wounded 5,752 other, while some 120,000 people have been displaced.
Libya has been wracked by chaos since the 2011 uprising and an ensuing NATO intervention in which longtime leader Muammar Gaddafi was killed. Haftar's offensive has exacerbated the crisis, threatening to plunge the country into a full-blown civil war.
Since Gaddafi's ouster, Libya has been divided mostly between two main rivaling powers, one linked with Haftar in the eastern city of Tobruk, and the other in Tripoli.