Oil tanker Kriti Samaria has been approved for entry into Libya's Zueitina port on Thursday evening or Friday to load 600,000 barrels of crude oil and will head to Italy, engineers told Reuters.
The tanker will be permitted to load oil from storage, the engineers said, without providing further detail.
Libya's two legislative chambers said on Tuesday they had agreed a mechanism for resolving the dispute over control of the central bank.
Libyan crude exports have been largely shut for more than a week amid a political showdown over control of the central bank, which is the sole legal depository for Libyan oil revenue and pays state salaries across the country.
Another tanker, the Front Jaguar, was loading crude from storage at Libya's Brega port, engineers told Reuters on Wednesday.
The crisis was triggered when western factions moved on Aug. 18 to oust veteran central bank governor Sadiq al-Kabir, who has since fled the country. Eastern factions responded by declaring a shutdown to all oil output on Aug. 26.
The National Oil Corporation, which oversees the country's oil resources, said on Aug. 28 that total oil output had dropped by more than half from typical levels to just over 590,000 bpd. It was not immediately clear where current production stood.
A member of the Organization of the Petroleum Exporting Countries (OPEC), Libya produced about 1.18 million barrels per day of crude in July, according to OPEC, citing secondary sources.