Protesters, who say they are frustrated over pay and transparency, have blocked the entrance to the Arabian Gulf Oil Co. in Benghazi for more than a week.
Abdul Jalil Mayuf, a spokesman for the company, told Bloomberg News that oil production might stop by Thursday if demonstrators aren't cleared.
"If this is not dealt with, then the consequences would be grave. It is unbelievable that a company as big as AGOCO remain hostage to a group of people," he said. "The government should either deal with them by force or find a solution."
Libyan oil production nearly halted during last year's civil war. The country was one of Africa's top oil producers before the conflict, averaging about 1.6 million barrels a day.
Mayuf said production at the Benghazi company could reach about 425,000 bpd by the middle of May.
The interim government in Libya is preparing for summer elections, the first in a generation. Tribal feuds and autonomy bids, however, are threatening the post-war political transition.
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