Libya is being racked by factional violence as the armed groups which helped topple Muammar Gaddafi in 2011 turn their guns on each other in a struggle to dominate politics and the country's vast oil resources.
In Benghazi, forces of retired general Khalifa Haftar have been fighting brigades including Ansar al-Sharia, blamed by Washington for an attack on the US consulate in September 2012 in which the US ambassador was killed.
On Saturday, militants were trying to seize the Benina area, home to a civilian and military airport under the control of Haftar's forces. They have already overrun several army camps this month.
Grad rockets hit the civilian airport, military sources and residents said. At least 10 soldiers from Haftar's forces were killed and 25 wounded, a hospital medic told Reuters.
Western powers worry Libya will become a failed state as a weak central government cannot control the competing armed groups in a country awash with arms.
Senior officials and the elected parliament have relocated to the remote eastern city of Tobruk after effectively losing control of the capital Tripoli, where an alliance of armed groups rules after expelling a rival force.
The new forces controlling Tripoli, led by brigades from the western city of Misrata, have helped install an alternative parliament and prime minister.
In a televised speech, Omar al-Hasi, not recognized as prime minister internationally, said his government wanted to lead Libya out of crisis and seek national reconciliation.
"We reject extremism and terrorism," he said. "I am not with a specific group, party, operation or city but stand for a government for all Libyans."
Adding to the sense of chaos, the Tobruk-based government issued a separate statement, calling on all militias to leave Libya's cities.