Forces from the city of Misrata claim control of Tripoli's main airport after more than a month of fighting with a rival group.
If independent sources confirm the airport has changed hands, it would be a major defeat for the nationalist fighters from Zintan west of Tripoli who have held the airport since the fall of long-time dictator Muammar Gaddafi in 2011.
A spokesman for the Islamist coalition, partly comprising men from Misrata, said its fighters "have entered the airport and are mopping up pockets of resistance". Pictures on social media this weekend purportedly showed Misrata fighters celebrating at the terminal building and standing on civilian planes.
Arab channels Al-Jazeera and Al-Arabiya also said Misrata forces were in control of the airport on Saturday.
Heavy shelling could be heard in other parts of the city.
Earlier, war planes had struck Misrata positions in Tripoli in an attack claimed by renegade general Khalifa Hifter. The raids killed 10 people and wounded dozens, the Misrata faction said.
The fighting is the worst since the overthrow of Gaddafi.
In the Nato-backed campaign to oust Gaddafi, fighters from the western region of Zintan and Misrata, east of Tripoli, fought together, but they later fell out and this year have turned parts of Tripoli into a battlefield.
Hifter launched a campaign against Islamists in the eastern city of Benghazi in May and threw his weight behind the Zintan fighters.
Tripoli television channel al-Nabaa said planes had attacked four Misrata positions. A Misrata spokesman said the planes were from Egypt and the United Arab Emirates, countries which have cracked down on Islamists.
But Hifter's air defence commander, Sager al-Jouroushi, said that his forces were responsible for the attack. Hifter's forces also claimed responsibility for air raids on Misrata positions in Tripoli on Monday.
Western countries and Egypt, fearing Libya becoming a failed state and haven for Islamist militants, have denied any involvement. The Libyan government has said it did not know who was responsible for the air attacks.
In a challenge to the parliament elected on June 25, the spokesman for radical group Operation Dawn called for the old General National Congress to be reinstated. Misrata forces have rejected the new house of representatives, where liberals and legislators campaigning for a federalist system have made a strong showing.
In a sign of deep divisions between political factions the house of representatives declared Operation Dawn as well as militant Islamists such as the Ansar al-Sharia "terrorist groups".
"This is a war between the Libyan state and the state institutions led by our sons, soldiers and officers in the army, against terrorist groups outside of the law," the house said in a statement.
Prime Minister Abdullah al-Thani called on Egypt and Tunisia to reopen air space for flights to western Libya. Both countries cancelled most flights to Libya for security reasons after the air strikes, cutting off a key link to the outside for Libyans and foreigners fleeing fighting.
The violence has prompted the UN and foreign embassies in Tripoli to evacuate staff and citizens, and most foreign airlines stopped flying to Libya.
Tripoli has slipped out of control of the government, with senior officials working from Tobruk in the east, where the new parliament has based itself to escape the violence.
Libya's central government lacks a functioning army and relies on militia for public security. But while these forces receive state salaries and wear uniforms, they report in practice to their own commanders and towns.