* Militia factions fighting for past month
* Neither side believed to have an air force
* U.S., Egyptian, NATO officials deny involvement
* Libyan government armed forces largely helpless (Adds fighting in Benghazi)
By Heba al-Shibani and Ayman al-Warfalli
TRIPOLI/BENGHAZI, Libya, Aug 18 (Reuters) - Renegade General Khalifa Haftar's air force was responsible for strikes on Islamist-leaning militia in Tripoli on Monday, one of his commanders said, after weeks of fighting for the capital in Libya's worst violence since Muammar Gaddafi was toppled in 2011.
Fighters from Misrata - east of Tripoli - have been battling militia from the western Zintan region for weeks and have thrown the North African state into anarchy. Zintanis and Misratis worked together to topple Gaddafi but have fallen out since.
The fighting hitherto has been limited to ground action with artillery and rockets. None of the militias had been thought to own warplanes, while the central government has only an outdated air force, badly in need of repair.
Libyan television news channels speculated that the country's neighbours might be behind the overnight air strikes, which Tripoli official Mohammed al-Kriwi said had killed about five people and wounded as many as 30.
A U.S. official and an Egyptian security source, both speaking on condition of anonymity, said their countries had not been involved. A NATO official said: "There are no fighter jets under NATO command involved in operations over Libya".
NATO air strikes helped rebels overthrow Gaddafi.
The air attacks escalate a struggle between Islamist and more moderate forces as well as between militias from different cities all vying for power in the oil producer. Central government has no control of either Tripoli or Benghazi.
Forces from Zintan had allied themselves with Haftar and stormed parliament in May, saying it had an Islamist agenda.
Referring to Haftar's campaign against Islamists which he had launched in Benghazi in May, his air defence commander, Saqer al-Jouroushi, told Reuters on Monday: "We, the Operation Dignity, officially confirm to have conducted air strikes on some militias' locations belonging to Misrata militias."
Clashes between Haftar's forces and Islamist fighters also broke out in Benghazi around 5 p.m. (1500 GMT) with one of his helicopters opening fire. A Reuters reporter at the scene heard loud explosions. Eleven of Haftar's men were taken to hospital, a military source said.
JETS HEARD AFTER MIDNIGHT
Tripoli residents said they heard several jets overhead after midnight, followed by loud explosions. No more planes were heard but fighting resumed in parts of the city in the morning.
A Zintani source said fighters in his unit saw planes bombing a Misrata militia position. "Our forces at the airport saw massive and accurate bombings," he said. Reuters reporters were not immediately able to access the area.
The Tripoli government said it did not know to whom the warplanes belonged. "The government does currently not have any convincing indications to establish which side was behind this," it said in a statement.
The central government of the OPEC member state has no functioning national army and most officials working from Tobruk in Libya's far east where the new parliament has set up to escape the violence.
An Egyptian security source said air traffic between the two countries had been interrupted for six hours and that Libyan air controllers had cited security reasons.
Some Tripoli residents, tired of daily fighting disrupting power and food supplies, hope NATO will intervene in Libya.
On Sunday, the U.N. Mission in Libya said it "deeply regrets that there was no response to the repeated international appeals and its own efforts for an immediate ceasefire".
The new U.N. special envoy, Bernardino Leon, who is due to start his job on Sept. 1, said he might travel to Tripoli as early as this week. (Additional reporting by Feras Bosalum, Ulf Laessing, Asma Alsharif and Arshad Mohammed; Editing by Louise Ireland)