At least 36 people have been killed in clashes between Libyan government troops and Islamist militants in the city of Benghazi, reports say.
The attack came as the militants attacked troops in the city centre.
Intense fighting near Tripoli airport killed another 23 people, reports say.
Militias controlling large parts of the country are responsible for Libya's worst violence since the 2011 uprising that toppled Col Muammar Gaddafi, correspondents say.
The US and the UK have advised their nationals not to travel to Libya.
On Saturday, the US evacuated its embassy in the capital, Tripoli, citing a "real risk" because of the fighting.
Earlier this week, the UN also announced it was withdrawing all its staff from Libya.
With no army, Libya's central government has increasingly lost control over the country to rogue and powerful militias in the last two years, says the BBC's Rana Jawad in Tripoli.