Footage released by the Libyan National Army (LNA) on Wednesday purportedly shows LNA forces reportedly in control of the Al Azizyah region, an area south-west of Tripoli.
Fighters from the LNA, led by Field Marshal Khalifa Haftar, can be seen celebrating and seizing abandoned military vehicles.
Since erupting over a week ago, fighting over the Libyan capital between Misrata forces and the LNA has left at least 47 dead, including 9 civilians.
The LNA, which controls eastern Libya, is aiming to take over territory from the internationally-recognised Government of National Accord (GNA) including Tripoli, as the country has been split between the two rival governments since 2014.
Approximately 4,500 Tripoli residents have so far been displaced due to the ongoing clashes, according to the UN Office for the Co-ordination of Humanitarian Affairs (UNOCHA).