Tankers were docking at the eastern Ras Lanuf, Es Sider, Zueitina and Brega ports as well as the western Zawiya terminal linked to the El Sharara field, they said.
Only the western Mellitah port remained closed because of bad weather, the shipping source said.
NOC could not be reached for immediate comment.
The company had said on Friday that production was down by 150,000 barrels per day (bpd), with a a further drop of 50,000 bpd expected because of a lack of storage capacity. Storage tanks at Es Sider are expected to fill within two days.
Production from the country's Sharara oilfield, which exports crude from Zawia, is expected to fall by 150,000 bpd if the bad weather persists, NOC said on Friday.
Libyan oil production recently hit a five-year high of
about 1.3 million bpd.
(Reporting by Ayman al-Warfalli and Ahmad Ghaddar; Writing by Ulf Laessing; Editing by David Goodman)
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)