Libya has been run by two governments and two parliaments since August, when an Islamist-backed militia alliance overran the capital Tripoli.
The government recognised by the international community fled to the country's far east and set up in the city of Tobruk.
The National Oil Corporation, founded in 1970, is based in Tripoli where Libya's Central Bank -- the depositor of the country's oil wealth -- also has its headquarters.
The NOC and Central Bank have so far remained neutral in the conflict, continuing to operate independently of any administration.
But, cut off from vital funding, the Tobruk government announced last month the creation of a rival corporation -- the National Oil Company -- in second city Benghazi.
It took another step on Saturday, instructing the company to begin exporting crude, to open a bank account in the United Arab Emirates and to set up offices in Britain, Germany and the United States.
The chairman of the Benghazi-based NOC, Mabrook Abu Seif, told AFP that it had already begun negotiating with oil firms that have contracts with its Tripoli rival.
Abu Seif did not name the companies or provide details on the nature of the talks, but he insisted that old contracts would be "respected and implemented once obstacles are removed".
- 'Deepen divisions' -
Still, experts said those obstacles would be difficult to overcome, with international oil traders unlikely to stop transactions with the Tripoli-based NOC after decades.
"Creating a rival NOC in Benghazi creates a whole new level of complexity and uncertainty for oil buyers," said Valerie Marcel, an associate fellow at Chatham House.
"I expect only the big risk-takers to sail to the new NOC's terminals," she said.
"Foreign oil companies have dealt with NOC in Tripoli for decades. They won't switch their business now," said Ibrahim Suleiman, an economics professor in Benghazi.
"The government has no other choice but to accept the status quo."
The Tripoli-based NOC and Central Bank have struggled to stay neutral in the conflict that has wracked Libya since veteran dictator Moamer Kadhafi was toppled and killed in a 2011 uprising.
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Libya has slid into chaos, with former rebels and powerful tribes vying for power in the North African country, where oil reserves are estimated at about 48 billion barrels.
Suleiman said the creation of a rival NOC will only worsen the country's crisis, as talks on forming a unity government have faltered.
"It will deepen divisions," Suleiman said.
"I don't believe that the international community will accept that. Most probably it will continue working with the company in Tripoli, and the Central Bank will remain neutral," he said.
Khaled Abdullah, a financial adviser for private oil firms in Libya, said drawing the bank into the conflict between Libya's rival factions was a mistake.
"The decision taken by the government could backfire," he said, adding that attempts to take revenues away from the Central Bank could see it "take sides and give money to the Tripoli government" from its $90 billion in reserves.
- 'A risky move' -
A spokesman for the Tripoli-based NOC said its new rival's efforts were bound to fail.
"All of the data and technical documents" are in Tripoli, spokesman Mohamed al-Harari said, referring to contracts, client information and documents such as oil maps.
"In the short run at least, it will make work for them difficult," he said.
Saturday's decision by the Tobruk government to start exporting oil came after fighters loyal to the Tripoli administration pulled out of the so-called "oil crescent" in the centre of the country.
The region, between Benghazi and Tripoli, is Libya's oil hub and home to key export terminals which Islamist rebels tried but failed to seize during deadly clashes with loyalists that erupted in December.
Oil is Libya's main natural resource, with a pre-revolt output capacity of about 1.6 million barrels per day, accounting for more than 95 percent of exports and 75 percent of the budget.
But unrest has forced a slump in production to about 350,000 bpd.
Richard Mallinson, an analyst with Energy Aspects, said the move would leave oil industry players with major questions.
"I think it is a risky move as it may disrupt the position the NOC and the Central Bank have managed to establish, balanced between the two rival governments," he said.
"If they (buyers) start to deal with a new entity does that mean sales by the NOC are not legitimate and what happens with ports not under the direct control of the Tobruk-based government?"