Output, which fell to 146,000 bpd on Wednesday, will rise further on Friday to between 200,000 bpd and 220,000 bpd if the power supply remains stable, a company official said, asking not to be identified. That would still be below a recent average of up to 260,000 bpd.
Libya's Raguba oilfield, which is operated by Sirte Oil company and produces 5,000 barrels a day, also resumed pumping crude to the eastern port of Brega after a protest stopped flows on Wednesday, a port official said on Thursday.
AGOCO and Sirte Oil are both subsidiaries of the state-run National Oil Corporation (NOC).
AGOCO was forced to halt production at the Massala field on Wednesday after temperatures reached 49 degrees Celsius, hitting power supplies, while the Sarir field had similar problems.
Libya, a member of the Organization of the Petroleum Exporting Countries, has not released its oil production figure for months. Industry sources had put it at 1 million bpd before the power cut hit AGOCO.
At the Raguba oilfield, a Sirte official said youths demanding improved state services who had blocked production had ended their blockade after the company intervened.
Protesters in the remote Marada region of eastern Libya, home to the Raguba and other oil assets, have frequently staged protests, demanding that authorities urgently deal with grievances over the absence of government, a shortage of healthcare and other services.
"We convinced the youth that oil production was needed to execute development projects," the official said after the meeting between Sirte, local officials and protesters in Brega.
Libya has been in turmoil since the toppling of leader Muammar Gaddafi in 2011.
Some youths had also protested about a lack of road links from Marada town to other communities and demanded jobs, officials have said, a common grievance in Libya.
Armed groups have twice blown up the pipeline near Marada since December as security in the remote eastern area is volatile.