Libya's National Oil Corporation (NOC) has evacuated staff from both the Sidra and Ras Lanuf terminals due to armed clashes in the area.
It said the loss in oil production is around 240,000 barrels per day (bpd) and a planned tanker berthing at Sidra was postponed on Thursday.
NOC bosses are following the situation closely.
"The NOC board has called for individuals or political groups who attempt to capture Libya’s oil installations, blockade production, or attempt to make NOC a bargaining chip, to be brought to justice," it said.
Minerva Marine's 104,000-dwt aframax Minerva Lisa (built 2004), which was due to arrive at Sidra to load a crude cargo on Thursday, was advised to stay outside the port, a source told Reuters.
The ship, chartered by trader Petraco, was seen turning away from the port on Thursday morning without loading, according to Reuters ship tracking.
A second tanker, Thenamaris' 105,000-dwt Seascout (built 2004), is expected to arrive at the port on 18 June.
Reuters said attacks had taken place by armed brigades opposed to the eastern commander Khalifa Haftar.
At least one storage tank at Ras Lanuf was set alight.
The clashes between forces loyal to Haftar's Libyan National Army (LNA) and rival armed groups were taking place south of Ras Lanuf, where the LNA was targeting its opponents with air strikes.
The LNA took control of the two ports in 2016, allowing them to reopen after a long blockade.
More than half the storage tanks at both terminals were badly damaged in previous fighting and have yet to be repaired, though there have been regular loadings from Sidra.
