Fresh battles have been broadcast near the Libyan capital Tripoli, between pro-government forces and hunters from the east of the country.
Reports say that clashes between the Gen Khalifa Haftar rebels and pro-government groups are taking place in three suburbs south of the city.
Tripoli is the basis of the UN-supported, internationally recognized government.
The UN Libyan envoy has insisted that a planned conference on possible new elections should still take place.
In a television speech, the head of the UN-backed government, Prime Minister Fayez al-Sarraj, accused Gen Haftar of committing a coup.
Mr Al-Sarraj said that his government "had extended our hands to peace", but said General Haftar will now "only receive strength and steadfastness".
- Why is Libya so lawless?
- Who is the military strong man Khalifa Haftar?
Libya has been torn apart by violence and political instability since the long-time ruler Muammar Gaddafi was deposed and killed in 2011.
What is happening on the ground?
General Haftar – who was appointed head of the Libyan National Army (LNA) under a previous UN-backed government – ordered his troops to go to Tripoli on Thursday, because UN Secretary General Antonio Guterres was in town for the continuing discuss the crisis.
The Libyan Air Force, nominally under government control, aimed Saturday morning at an area 50 km south of the capital.
It is unclear whether there were casualties, but the LNA vowed to retaliate.
Fighting has taken place in various areas, including near the disused international airport south of Tripoli.
Gen Haftar spoke to Mr. Guterres in Benghazi on Friday, and reportedly told him that his operation would not stop until his troops had defeated "terrorism."
Tripoli residents have begun to stock up on food and fuel, AFP reported.
Earlier this year, LNA troops seized southern Libya and its oil fields.
What has been the reaction?
The G7 group of large industrialized countries has urged all parties to "immediately stop all military activities". The UN Security Council has made a similar call.
Russia has also called on parties in the escalating conflict to reach an agreement.
Speaking in Egypt, Russian Foreign Minister Sergei Lavrov warned of what he called foreign interference in Libya, while Egyptian Minister Sameh Shoukry said that Libya's problems cannot be solved by military means.
Both countries have supported Gen Haftar.
UN envoy Ghassan Salame said on Saturday that the conference scheduled for April 14-16 would still be held on time despite the escalation – "unless compelling circumstances force us not to do this".
Longed for a political solution?
By Sebastian Usher, BBC Arab business editor
It is still unclear to what extent this is a power sport to strengthen Gen Haftar's position or a real attempt to seize Tripoli.
He returned during the revolution and he then became the most powerful military leader in a country full of militias, allied to a rival government in the east.
Despite the chorus of international concern about his actions, he has received the support of powerful external players, including the UAE and Egypt.
Efforts for a political solution for Libya have failed time and time again. The most recent hope may have been stroked again.
Who is Khalifa Haftar?
Born in 1943, the former army officer helped Colonel Muammar Gaddafi to seize power in 1969 before he fell apart with him and went into exile in the US. He returned in 2011 after the uprising against Gaddafi began and became a rebel commander.
In December, Haftar met Prime Minister Fayez al-Serraj of the UN-backed government during a conference but refused to attend official discussions.
He visited Saudi Arabia last week, where he met King Salman and Crown Prince Mohammed bin Salman for conversations.