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"The country's production is rising constantly and should return to its level prior to this year if the situation stabilises in the various oilfields," interim Oil Minister Omar al-Shakmak told AFP.
Mohamed Hrari, spokesman for Libya's National Oil Corporation (NOC), said: "Production on Monday reached 550,000 barrels, up from around 400,000 barrels a day previously."
In a statement to AFP, Hrari forecast "a production level of one million barrels a day (bpd) in September, with an increase in production in the Sharara and Al-Fil (southwest) fields and a resumption of production in other fields in the east, west and south of the country."
Though Libya is currently wracked with violence between well-armed rival militias, the government announced on July 6 that the 200,000 bpd Ras Lanuf and 350,000 bpd Al-Sidra terminals were ready to resume exports.
The announcement was possible following an agreement unveiled four days earlier for rebels to hand back the two terminals in eastern Libya to government control.
The block on the two other eastern terminals, 110,000 bpd Al-Hariga and 100,000 bpd Zueitina was lifted in April but exports have been slow to take off.
Separatist security staff at ports in eastern Libya had prevented all exports since July 2013.
A first export cargo of 690,000 barrels of crude left Ras Lanuf, 700 km (400 miles) east of Tripoli, last week bound for Italy, Hrari said.
Another cargo should leave Al-Sedra terminal "probably next week," he said.
Libya's return to the market has hit oil prices, which slumped to a four-month low in London on Monday before recovering in Asian trade on Tuesday.
Libya may be plunged in chaos, but it has managed to step up daily output from 200,000 to 450,000 bpd, analysts at PVM brokerage in New York said on Monday.
The reopening of Ras Lanuf is a major sign of progress and indicates that Al-Sidra is likely to reopen soon, they added.
Shakmak, the interim oil minister, said: "Libya lost many customers on the oil market while exports were halted for a year.
"These customers went elsewhere," he said, adding: "Libya has managed to win some of them back."
Libya "is trying to regain traditional customers and find new ones, and we will get there," Shakmak said optimistically.
A tanker with 600,000 barrels capacity will arrive "in the next two days at Al-Sidra to take a shipment," said Samir Kamal, NOC's director of oil and gas.
He told AFP that tanks at the terminal currently contain 6.5 millon barrels of crude, stored during the crisis, while Ras Lanuf has 4 million barrels in storage.
"All terminals in the country are in working order except Zueitina, shut because of industrial action we are trying to settle," Kamal said.
The oil crisis has cost Libya $40 billion in lost income this year, specialists say.
The strife led to production dropping to 250,000 bpd from a peak of 1.5 million bpd before the 2011 fall of long-time dictator Moamer Kadhafi.