At least 36 people were killed in Libya's eastern city of Benghazi, many of them civilians, in clashes between Libyan Special Forces and Islamist militants last night and this morning, medical and security sources said.

Another 23 people, all Egyptian workers, were killed in the capital Tripoli when a rocket hit their home yesterday during clashes between rival militias battling over the city's main airport, the Egyptian state news agency reported.

In the last two weeks, Libya has descended into its deadliest violence since the 2011 war that ousted Muammar Gaddafi, prompting the United States, the United Nations and Turkey to pull their diplomatic staff out of the North African country.

With the central government unable to impose order, two rival militias are fighting in Tripoli, while army units are trying to push out Islamist militants who have set up camps on the outskirts of Benghazi.

The United States evacuated its embassy in Libya yesterday, driving diplomats across the border into Tunisia under heavy military escort after escalating clashes broke out near the embassy compound in Tripoli.

Libya's western partners worry the OPEC oil-producing country is becoming increasingly polarized between the two main factions of competing militia brigades and their political allies, whose battle is shaping the country's transition.