A statement by the provisional government, which lacks any real authority, said it was not known whose aircraft had attacked militia positions.
However, an aide to rogue general Khalifa Haftar, who has launched an offensive against Islamists in second city Benghazi, said the aircraft had been sent by him.
Saqr Jarouchi, also a dissident general, later told AFP: "Those were our planes that launched raids."
But an air force unit that has refused to join Haftar's offensive in the eastern city of Benghazi dismissed the claim, saying the aircraft were "foreign, not Libyan".
Also Read
The mystery aircraft first flew over at around 2:00 am (local time) and a resident told AFP he heard a loud explosion which was followed by others.
"The explosions were clearly heard in eastern districts of Tripoli, 15 kilometres from the town centre," he said.
Television channel Libya Awalan (Libya First), which is close to Haftar, said: "Military planes bombarded various positions" near Tripoli. It gave no further details.
The airport has been closed since July 13 and is in the hands of militiamen from Zintan, southwest of Tripoli.
They have been fending off a challenge from the fighters from Misrata, east of the capital, for control of a bridge giving access to the airport.
Haftar in May launched an offensive dubbed "Operation Dignity" against radical Islamist groups which have held sway in Benghazi since the fall of long-time dictator Moamer Kadhafi in 2011.
"These parties must stop fighting, agree to talk and withdraw from Tripoli and other Libyan towns," the statement said, adding that the government had been in contact with "friendly" states to try to identify the aircraft.
France denied what it called rumours of French involvement in air strikes.
"Rumours of air raids in Libya in which France was involved are wrong," the foreign ministry spokesman said in Paris.