Report from BBC say rebel forces loyal to Khalifa Haftar are near the outskirts on three sides, about 25km (15 miles) from the centre.
Tripoli is the base of the UN-backed, internationally recognised government.
The UN’s Libya envoy has insisted that a planned conference on possible new elections will still go ahead.
Why is Libya so lawless?Who is military strongman Khalifa Haftar?
UN troops in the capital have been placed on high alert.
Libya has been torn by violence and political instability since long-time ruler Muammar Gaddafi was deposed and killed in 2011.
What’s happening on the ground?
General Haftar – who was appointed chief of the Libyan National Army (LNA) under an earlier UN-backed administration – ordered his forces to advance on Tripoli on Thursday, as UN Secretary General Antonio Guterres was in the city to discuss the ongoing crisis.
They have been fighting in several areas, including near the disused international airport south of Tripoli.
The LNA said it had been targeted by air strikes to the south of Tripoli by a plane that had taken off from Misrata. Pro-government forces in Tripoli said they had launched “intensive strikes”. Source Bbc