On Saturday, armed forces of the internationally recognised government tried to push back a convoy of militia loyal to Fathi Bashagha, the man who a rival, eastern parliament recognises as prime minister.
There is reports of small-arms fire and explosions in several areas of the capital. Black smoke have seen rising across the city.
Emergency services said a number of hospitals has been full. People were also evacuated from areas around the fighting.
The UN's Libya mission said the fighting has included "indiscriminate medium and heavy shelling in civilian-populated neighbourhoods" and called for an immediate ceasefire.
The oil-rich country once had one of the highest standards of living in Africa, with free healthcare and free education.
But the stability that led to its prosperity has been shattered and Tripoli has seen frequent fighting between rival forces since 2011.