Agoco's Abdeljalil Mayuf said by phone said Agoco hoped to reach full production of 425,000 bpd by the end of February.
Mayuf said output at the Sarir field was at 130,000 bpd, while Messla was producing 83,000 bpd. Production was 35,000 bpd at Nafoora, 5,000 bpd at Hamada and 13,000 bpd at Beda, he said.
"Hamada is at half of its production," Mayuf said.
Agoco, a subsidiary of Libya's National Oil Corporation (NOC), was the first to restart production in Libya after around seven months of war.
The bulk of Libyan export tankers have so far been sold by Agoco from Tobruk, which was left unscathed by the conflict.
Mayuf said he did not give specifics on how many crude cargoes Agoco intended in the weeks ahead. "In the last month, it was almost one tanker a week," he said.
Agoco took charge of selling the small amount of oil that Libya exported and all oil product imports during the eight-month war after sanctions impaired the NOC's operations.
A NOC source said last week it had now taken over responsibility for selling the oil, but Agoco was not immediately available to confirm this.
"There are discussions; up until now we are still in charge of marketing operations," Mayuf said.