The struggle in the capital is part of worsening chaos in the North African country where rebels who helped to topple Muammar Gaddafi in 2011 now vie for power and a share of Libya's oil wealth. Militias from the city of Misrata and fighters allied to the western town of Zintan have wrestled for control of the capital in the worst clashes since the NATO-backed uprising.
Through the day gunfire and shelling could be heard near the airport and other parts of Tripoli, but the fighting was less fierce than on Saturday when much of the city was a battlefield. The battles have forced the United Nations and Western governments to evacuate their diplomats, fearing Libya is sliding into civil war.
The UN Mission in Libya said in a statement that it "deeply regrets that there was no response to the repeated international appeals and its own efforts for an immediate ceasefire". "The Mission warns that the continued fighting poses a serious threat to Libya's political process, and to the security and stability of the country," the UN said.
On Friday, the new UN special envoy Bernardino Leon, who is due to start his job officially on Sept. 1, said he was aiming to end fighting and might travel to Tripoli as early as next week.
Most of the fighting has raged over the international airport in Tripoli, which fighters from Zintan have controlled since sweeping into the capital during the 2011 war.
Libya's fragile government still has no national army and often put former rebels on the state payroll as semi-official security forces as a way to co-opt them into the new state. But the heavily armed rival brigades are allied with competing political factions and are often more loyal to their region, city or local commanders than to the central government.
A separate battle in the eastern city of Benghazi has complicated Libya's security, with an alliance of Islamist militants and ex-rebels forcing the army out of the city.
A group of Islamists in Benghazi including Ansar al-Sharia issued a statement on Sunday rejecting the idea of democracy and secular political parties in Libya. "We don't fight for the sake of democracy...but for God and to defend the land," the statement said.
Three years since Gaddafi's rule ended, Libya's fragile efforts towards democracy are close to chaos. The month of fighting in Tripoli and Benghazi has further polarised the political factions and their militia allies.