South of Tripoli, fierce fighting erupted after the UN-backed Libyan government announced a counter-offensive against the insurgents.
It came in clashes after days of limited thrust on both sides, in which 220 people died.
General Khalifa Haftar had launched an attack earlier this month with the goal of taking Tripoli.
Prime Minister Fayez al-Serra has condemned the "silence" of his international allies during the fighting.
- Who is the strong military Khalifa Haftar?
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Details of the progress of both sides were not immediately clear.
The government of the national agreement of Mr. Serra says they have carried out seven air strikes on areas of the Libyan state of Gen Haftar Army (LNA).
The group has moved into the city from several directions and says it has taken over the international airport of Tripoli.
The UN-backed government says it launched a counter-offensive Gen Haftar forces.
Gen Haftar, a former army officer, was appointed head of the LNA in 201
He has support from Egypt, Russia and the United Arab Emirates.
The White House says President Trump spoke with Gen Haftar, suggesting that the US could also endorse a new government under his command.
Both America and Russia have refused to support a United Nations Security Council resolution calling for a ceasefire.
A spokesman for the LNA told AFP: "We have won the political battle and convinced the world that the armed forces are fighting terrorism."
Gen Haftar is supported by several foreign powers, which consider him as potentially stabilizing Seeing power in the chaos of Libya living after the revolution, reports BBC editor for Arab affairs, Sebastian Usher.
Some Libyans feel the same way, but others see him as another warlord who wants to gain power by force, our editor.
Libya has been torn apart by violence and political instability since long-time ruler Muammar Gaddafi was deposed and killed in 2011.