The convoy of Libya's contested unity government chief, Fayez al-Sarraj, came under gunfire in Tripoli on Monday, without causing any casualties, his administration said.

"The convoy of GNA (Government of National Accord) chief Fayez al-Sarraj... came under fire as it passed near the Abu Slim sector of Tripoli," said spokesman Ashraf al-Thulthi.

"All the cars were armoured-plated, and there were no injuries," he said, adding an investigation was underway to identify the assailants.

Sarraj's fragile GNA, formed under a UN-backed deal signed in late 2015, has struggled to impose its authority, particularly in eastern Libya where a rival administration holds sway.