A Libyan militia battling a rival armed group over control of the country's biggest airport is ready for a peaceful solution after five days of heavy fighting, a spokesman said, hours after shells hit the terminal building.

The news, if confirmed by the rival militia, would be a huge relief for Libyan citizens who were stunned after two armed groups turned Tripoli International Airport into a battlefield.

The conflict is fuelling worries that Libya is on the point of turning into a failed state where a weak central government is powerless to control militias that helped oust Muammar Gaddafi in a NATO-backed uprising in 2011 but now defy state authority.

"There is an agreement between the conflict parties on a ceasefire and to hand over the airport to a committee tasked by the prime minister (to find a peaceful solution)," said Mahmoud al-Hatwish, spokesman for the town council of Zintan.

The conflict has pitted fighters from Zintan in the northwest, who have controlled the airport since the ousting of Gaddafi, against armed groups from Misrata, a western coastal town.

There was no immediate comment from the Misrata brigades. A copy of an agreement posted on social media said both sides had committed themselves at a meeting brokered by the Tripoli town council to a ceasefire and withdrawal from the airport.

A "neutral" force from a different part of Libya would protect the airport in the future, according to the agreement's text.

The militias are no united front, making it difficult to keep agreements in a country awash with heavy arms.

Hours earlier several shells hit for the first time the main terminal where the Zintani forces are concentrated. Days of fighting had already damaged at least 20 civilian aircraft belonging to Libyan carriers, officials said on Wednesday.

A Reuters reporter at the airport saw holes in the roof and smashed windows at the terminal and in airline offices, including one belonging to British Airways, with a shell lying on the floor.

FEMALE MP KILLED

In another sign of turmoil, air controllers halted work in Tripoli, shutting off much of the oil-producing country from international traffic.

On Wednesday, Libya reopened the western Misrata airport, which had been closed with Tripoli after the weekend attack, but it will have to shut again because Tripoli air controllers are also responsible for Misrata.

But late on Thursday a passenger plane could be seen circling over Tripoli though it was not clear from where it had taken off. A transport ministry spokesman said he had no information about the plane.

Libyans who had been planning to come home for the Muslim fasting month of Ramadan have been trapped abroad. Expatriates trying to leave the country have been travelling by taxi to Tunisia, in scenes reminiscent of the 2011 NATO-backed uprising.

In the eastern Islamist hot spot of Derna, gunmen shot dead Fariha al-Barkawi, a former member of parliament, officials said. She is the second prominent woman to be assassinated, following the killing of Benghazi human rights activist Salwa Bugaighis last month.

Western powers fear chaos in Libya will allow arms and militants to flow across its borders. The south of the vast desert country has become a haven for Islamist militants kicked out of Mali by French forces earlier this year. - Reuters