Four ports in Libya's so-called oil crescent were seized this week by forces led by Field Marshal Khalifa Haftar, in a major blow to the UN-backed Government of National Accord.
Haftar backs a rival administration in the country's east.
"Exports will resume immediately from Zuwaytina and Ras Lanuf, and will continue at Brega," said NOC chairman Mustafa Sanalla in a statement on the company's website.
"Exports will resume from Al-Sidra as soon as possible."
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Libya, which has Africa's largest oil reserves, has only managed to export a few tankers of crude in recent months, with efforts to revive the industry thwarted by jihadist attacks and political turmoil.
Haftar's seizure of the ports raises the prospect of renewed oil exports from Libya, whose crude reserves are estimated at around 48 billion barrels.
The NOC considers itself loyal to the GNA, but also to the country's internationally-recognised parliament, which supports Haftar's forces.
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