Oil industry executives say Zeidan's shaky central government risked widening violence that could descend into civil war if it uses force to recapture oilfields.
Libya's oil production has fallen further to around 150,000 barrels per day (bpd) - from around 1.4 million bpd in April - confined to offshore rigs protestors cannot reach, a National Oil Corp (NOC) official said.
Armed groups have also threatened to close the Wafa gas field, which if shut would cause severe power shortages in the capital, an oil official told Reuters.
Wafa, in the south west, is the only major gas field left open to supply power stations. Libya is importing much more diesel and fuel oil for electricity plants that previously relied on gas.