The renewed fighting, which killed at least five civilians, was condemned by the European Union, which urged restraint and dialogue.
A coalition of militias led by Islamist fighters launched an assault on Tripoli international airport, with clashes later spreading to the road leading to the capital.
"The airport was attacked this morning with mortar rounds, rockets and tank fire," airport security official Al-Jilani al-Dahesh told AFP.
"It was the most intense bombardment so far," since a week-old battle for control of the airport erupted on July 13.
Islamist militias have been joined by other armed groups, including the powerful Misrata Brigades which played a key role in the 2011 UN-backed revolt that toppled and killed strongman Moamer Kadhafi.
The fighting has forced a halt to all flights and caused extensive damage to planes and airport infrastructure, with aviation officials saying Tripoli airport could stay closed for months.
Pictures posted on social media showed a Libyan Airlines plane on fire as plumes of smoke billowed over the airport.
By midday, fighting had spread to other sites on the airport road that are controlled by the Zintan militia, an AFP correspondent said.
Loud explosions were heard in the city centre, 25 kilometres (15.5 miles) away, as battles raged along the airport road with rockets striking nearby homes.
At least five civilians were killed in the Qasr Bin Ghashir neighbourhood, Mohamed Abderrahman from the local town council, told private Al-Nabaa television.
The rival sides are among several heavily-armed militias which have held sway in the oil-producing North African nation for the past three years.
The European Union mission in Libya issued a statement today urging fighters to lay down their arms and spare civilian lives.
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