Libya’s UN-backed government says 21 people have been killed and 27 wounded in fighting near the capital, Tripoli.
US Secretary of State Mike Pompeo has called for an immediate halt to the fighting and called for talks.
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.
Earlier the UN appealed for a two-hour truce so casualties and civilians could be evacuated, but fighting continued.
And in a statement, Secretary of State Pompeo said the US was “deeply concerned about fighting near Tripoli” and stressed the need for talks.
“This unilateral military campaign against Tripoli is endangering civilians and undermining prospects for a better future for all Libyans,” the statement said.
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.