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. The Libyan ngovernment has said it does not know who is responsible for the air attacks.
The North African oil producer has been in chaos as the weak government is unable to control former rebel factions which helped topple Gaddafi.
Prime Minister Abdullah al-Thani called on Egypt and Tunisia to open its airspace again for flights to western Libya. Both countries had cancelled most flights to Libya for security reasons after the air strikes, cutting off a vital link to the outside for Libyans and foreigners fleeing fighting.
"This has a negative impact on movements of Libyan citizens and puts an additional burden on all people," Libya's embassy in Cairo said in an statement.
Libya has used the small Matiga airport in Tripoli for civilian traffic since the main airport was turned into a battlefield last month. The tower, runway and at least 20 aircraft have been damaged, officials have said.
When flying into Matiga, passengers can sometimes see smoke rising from battles in and around the main airport.
The violence has prompted the United Nations and foreign embassies in Libya to evacuate their staff and citizens, and foreign airlines largely stopped flying to Libya.
Tripoli has largely slipped out of control of the government, with senior officials working from Tobruk in the far east, where the new parliament has based itself to escape the violence in Tripoli and Benghazi.
Libya's central government lacks a functioning national army and relies on militia for public security. But while these get state salaries and wear uniforms, they report in practice to their own commanders and towns.
© Thomson Reuters 2014