Medical sources told the BBC that at least eight people, including civilians, have been killed and more than 20 injured.
A new UN-backed Government of National Accord (GNA) still lacks authority and the country remains volatile.
The French Foreign Ministry said it was "very worried by the escalation of violence".
The BBC's North Africa Correspondent, Rana Jawad, in neighbouring Tunis, said two of the city's largest and most heavily armed militias are fighting an alliance of hard-line Islamists and militias loyal to rival political authorities.
Libya is still politically divided as rival administrations attempt to assert their power.
Clashes are said to be continuing in two main districts in the south of the capital. Tanks and pickup trucks armed with rocket launchers were reportedly deployed in several districts.
Witnesses told the BBC that people stayed at home on Friday morning and many businesses stayed closed.
The new government in Tripoli has not commented on the clashes.
East and central:
West:
Guide to Libya's militias
Profile: Khalifa Haftar
Rogue general divides Libyans

At least five vehicles are believed to have been involved in the collision at J18 Charing Cross.
Emergency services are at the scene and traffic is being directed off at J17, down Newton St and back on at J19, before the Kingston Bridge.
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Rival militias are battling one another in Tripoli in the heaviest fighting in the Libyan capital for two years.
[NEXT_CONCEPT]
The westbound M8 motorway has been closed in central Glasgow following a serious crash.