The 600,000-barrel oil tanker Front Jaguar was loading at Libya's Brega port on Wednesday, engineers told Reuters and Kpler data showed, despite a blockade that has halted other exports.
The tanker was permitted to load oil from storage after exports had been halted at major Libyan ports, the engineers said, without giving further details.
Crude exports at major Libyan ports have been shut for nearly a week and oil output has plummeted since eastern authorities in the divided country ordered a shutdown to all oil production on Aug. 26.
The eastern authorities' declaration was in response to western factions moving to oust veteran Central Bank of Libya (CBL) Governor Sadiq al-Kabir and replace him with a rival board.
Libya's two legislative chambers said on Tuesday they had agreed a mechanism for resolving the dispute over control of the CBL, which receives revenue from Libya's oil exports, the vast bulk of the national wealth.
Crude exports remained halted at Zueitina port on Wednesday but the 5,000 tons-capacity tanker Gaz United was expected to arrive there on Thursday to load propane, engineers there told Reuters on Wednesday.
The crisis over control of the CBL threatens to spiral and could end a four-year period of relative peace in the major oil exporter long split between factions in its east and west.
The National Oil Corporation, which controls Libya's oil resources, declared force majeure at the 70,000 barrels per day El Feel oilfield on Monday. Reuters had reported last week that output was halted there.
NOC said on Aug. 28 that total oil output dropped by more than half from typical levels to just over 590,000 bpd. It was not immediately clear where current production stood.
Reuters reported on Saturday that Libya's Sarir, Messla and Nafoura oilfields had been ordered to resume production by their operator, Arabian Gulf Oil Company, an NOC subsidiary.
About 150,000 barrels per day of output from Sarir and Messla was arriving at Hariga port for local consumption, while any excess was being stored, engineers at the fields said on Wednesday.
