Gen Khalifa Haftar’s fighters say they took control of the Ras Lanuf and Sidra terminals but the claim was denied by a militia guarding them.
The militia did confirm coming under attack on Sunday morning and said there had been a number of casualties.
Libya has been plagued by instability and infighting since the toppling of Colonel Muammar Gaddafi in 2011.
Oil production has dropped to about 200,000 barrels per day (bpd) from the 1.6m bpd it was producing before Gaddafi’s fall, Reuters news agency reports.
Gen Haftar, a former commander in Gaddafi’s army who later worked to topple him from exile, is one of the most powerful military figures in Libya.
He refuses to recognise the authority of the UN-backed Government of National Accord in the capital Tripoli, and is loyal to a rival government based in the eastern city of Tobruk.
The general leads the Libyan National Army, an umbrella group of army units and other forces loyal to them.
Ras Lanuf and Sidra together account for more than half of Libya’s output of oil.
A spokesman for the Petroleum Facilities Guard militia, Ali Alhassi, told the BBC the attack had started at 07:30 (05:30 GMT) and fighting had also been reported at Zuitina.
There were casualties but he could not give any confirmed numbers, he added.
Ahmed al-Masmari, a spokesman for Gen Haftar’s forces, told reporters they had taken Ras Lanuf and Sidra and were still fighting for Zuitina.
The UK Ambassador to Libya, Peter Millett, tweeted to say reports of fighting around Libya’s oil terminals were “worrying”.
Martin Kobler, head of the UN Support Mission in Libya, tweeted: “Worried about reported fighting in the oil crescent will add to division and further restricting oil exports. Oil belongs to all Libyans.” -BBC