At least 28 people have been killed since Thursday in fighting at Ras Lanuf and al-Sidra
The self-styled Libyan National Army loyal to strongman Khalifa Haftar announced on Sunday a "major offensive" to drive rival groups from the country's northeastern oil crescent.
Armed groups on Thursday attacked the Ras Lanuf and Al-Sidra terminals held by Haftar's forces around 650km east of Tripoli.
"We have launched a major offensive supported by the army and air force to drive out the militias of [Ibrahim] Jadhran and his allies", LNA spokesman Ahmed al-Mesmari told AFP.
Jadhran's Petroleum Facilities Guard controlled the terminals for years following the 2011 ouster and killing of long-time Libyan ruler Muammar Gaddafi, but were eventually forced out by the LNA.
The LNA controls most of eastern Libya and is opposed to an internationally recognised government based in Tripoli, which has itself condemned Thursday's militia attacks.
On Thursday, Jadhran said in a video that he had formed an alliance to retake oil terminals seized by Haftar's forces in September 2016.
The LNA's air force on Sunday told residents in the oil crescent to stay away from "areas where the enemy gathers, munition stores and sites with military vehicles".
"Fighter [planes] are carrying out raids against terrorist positions and gatherings in the operational military zone stretching from Ras Lanuf to the edge of the city of Sirte," the air force said on its Facebook page.
The Red Crescent in Ajdabiya, 150km east of Ras Lanuf, on Friday said it received 28 bodies, without specifying to which group they belonged.
The National Oil Corporation (NOC) on Saturday said a storage tank had been "significantly damaged" due to the armed incursions into Ras Lanuf and Al-Sidra.
It called for the "immediate and unconditional surrender" of Jadhran's militia to "prevent an environmental disaster and further destruction of key infrastructure".
The NOC on Thursday said it had halted oil exports from Ras Lanuf and Al-Sidra because of the violence.
NOC chief Mustafa Sanallah warned that if oil exports from these terminals remain at a standstill it could cause a "national disaster".
The oil firm warned on Friday that output could fall by up to 400,000 barrels per day if the export shutdown continues.
Libya's economy relies heavily on oil, with production at 1.6 million barrels per day under Gaddafi.
The 2011 uprising against Gaddafi saw production fall to about 20 percent of that level, before recovering to over one million barrels per day by the end of 2017.