NOC and an engineer at Es Sider port, which the pipeline feeds, said the fire had been brought under control in the early hours of Sunday.
In a Twitter post, NOC estimated the loss at between 70,000 and 100,000 bpd and said its firefighters are working at the scene.
The OPEC country's output has recovered in the last year to almost 1 million b/d, having dropped to as low as 300,000 b/d in the years following the 2011 revolution.
Libya's oil infrastructure has been repeatedly targeted by militants in recent years.
Back in December 2017, the Waha-owned pipeline was attacked and crippled in roughly the same area.
A Libyan oil source, speaking on condition of anonymity, said that at least some within the NOC found the price Total was paying too low. It previously announced plans to raise output to 600,000 b/d. This will depend on how long repairs take. The December attack closed the pipeline for around two weeks, but only resulted in a couple of days of delay to NOC's January program.
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