The faction under attack, Operation Dawn mainly from the town of Misrata, said the raids had killed 10 people and wounded dozens. Haftar launched a campaign against Islamists in the eastern city of Benghazi in May.
He threw his weight behind fighters from the western region of Zintan who are battling militia from the town of Misrata, east of Tripoli.
In the 2011 NATO-backed campaign to oust Muammar Gaddafi fighters from Zintan and Misrata were comrades-in-arms but they later fell out and this year they have turned parts of Tripoli into a battlefield.
Residents heard loud explosions early in the morning near the main airport where the two groups have been fighting for control for more than a month, in the worst fighting since the overthrow of Gaddafi.
Local television channel al-Nabaa said planes had attacked four positions of Operation Dawn. Mohamed Gharyani, spokesman for Operation Dawn, said also hit were buildings of state oil firm al-Waha near the airport road and the chief of staff headquarters under control of his forces.
Haftar's air defence commander, Sager al-Jouroushi, told Reuters that the general's forces were responsible for the attack. Haftar's forces also claimed responsibility for air raids on Operation Dawn positions in Tripoli on Monday.
After those raids Libyan TV channels speculated that the country's neighbours might be behind the attacks. Western countries and Egypt, worried about Libya becoming a failed state and safe haven for Islamist militants, have denied any involvement.