Libya’s UN-backed government says 21 people have been killed and 27 wounded in fighting near the capital, Tripoli.
Earlier the UN called for a two-hour truce so casualties and civilians could be evacuated, but it was unclear if there was any lull.
Rebel forces under Gen Khalifa Haftar have advanced from the east with the aim of taking Tripoli.
Prime Minister Fayez al-Serraj has accused him of attempting a coup and says rebels will be met with force.
Among the dead was a Red Crescent doctor killed on Saturday. Gen Haftar’s forces said they had lost 14 fighters.
International powers have begun evacuating personnel from Libya amid the worsening security situation.
Libya has been torn by violence and political instability since long-time ruler Muammar Gaddafi was deposed and killed in 2011.
What’s the situation on the ground?
Gen Haftar’s Libyan National Army (LNA) forces have been carrying out a multi-pronged attack from the south and west of the city since Thursday.
On Sunday the LNA said it had carried out its first air strike, a day after the UN-backed Government of National Accord (GNA) hit them with air strikes on Saturday.
Fighting has continued around the disused international airport south of the capital that Gen Haftar earlier said his forces had seized.
Forces loyal to the GNA have slowed the advance and on Sunday a GNA spokesman told Al-Jazeera TV that the GNA now intended to “cleanse” the whole of the country.