Army forces loyal to Libya's internationally recognized government have been fighting militant groups in Libya's second-largest city as part of a wider struggle since the overthrow of Muammar Gaddafi in 2011.
They have regained some territory lost last year. But progress has stalled as fighters of the militant Majlis al-Shura are still holed out in several districts and the port area despite claims by army commander Khalifa Haftar that his forces control almost the entire city.
"We are facing ammunition shortages in all parts of Benghazi," said Mohamed el-Hejazi, Haftar's spokesman.
He appealed for international help, saying: "We are fighting terrorism on behalf of the world."
Libya's official Premier Abdullah al-Thinni, working out of the east since losing the capital Tripoli to a rival faction in August, said on Sunday the U.N. should lift an arms embargo so his forces could buy weapons.
Libya has been under an arms embargo since the NATO-backed uprising against Gaddafi in 2011. Western powers have opposed lifting the ban as questions remain where the arms would end up in a chaotic situation, Reuters reported.
Libya has two governments allied to former rebel groups, while Gaddafi's regular army was largely destroyed in 2011.
The appeals to lift the arms embargo came after fighters of the Majlis al-Shura posted pictures on social media purportedly showing mortars and rockets they had produced locally.