Heavy gunfire was heard during Tuesday evening in the Ain Zara district on the south-eastern outskirts of Tripoli, according to reports from the AFP news agency.
The violence is reported to have already displaced thousands of people and left several dozen people dead.
Nearly half a million children in the Libyan capital are “at immediate risk”, according to the UN.
The Libyan National Army (LNA) led by Field Marshall Khalifa Haftar said it had taken control of an army barracks in the Aziziya area, some 50 kilometres south of Tripoli, AFP reported.
The LNA said several fighters loyal to the UN-backed government had been detained and weapons seized following “ferocious clashes”.
The Western-backed Government of National Accord (GNA) spokesperson Colonel Mohamed Gnounou said several airstrikes against the LNA were carried out south of Tripoli, according to AFP.
It appears that Haftar’s forces are advancing from the south and southeast of Tripoli, while roads to the east and west of the city are being held by GNA fighters.
Haftar has ignored calls from the UN Security Council and US to stop the long-anticipated attack on Tripoli.