Luaibi also confirmed exports from the semi-autonomous northern Kurdish region were expected to resume soon. But he said there was "nothing new" regarding a disagreement between Iraqi Kurdistan and the central government in Baghdad over contracts to develop the northern oil fields.
News reports last week had quoted Luaibi as saying Baghdad would honor the contracts, which Baghdad has repeatedly said it regards as illegal. Shares in Norwegian oil company DNO, which has such a contract, rose 9 percent on Monday after these reports.
Iraq sits upon some of the world's largest oil reserves but has struggled to push output close to the 3 million barrels per day it produced in the late 1980s, before it invaded Kuwait.
Luaibi said on Saturday that Iraq aimed to raise oil output to 3 million barrels per day by the end of 2011.
Luaibi, who was appointed to his new position last week, said on Friday that Iraq was on track to raise output capacity to 12 million bpd in six to seven years' time.
Skeptical analysts say 6-7 million bpd is a more realistic target. Reuters surveys of OPEC output found Iraq's daily output was 2.5 million barrels a year ago, but dipped in subsequent months.
On Monday, Luaibi told reporters: "Today the Iraqi production reached more than 2.6 million bpd for the first time in 20 years."
Lingering insecurity and months of political limbo have delayed much-needed upgrades to the war-ravaged country's oilfields and export pipelines.
Luaibi said Kurdish exports were expected to resume soon, but said there was no specific timeline.
Hussain Al-Shahristani, Iraq's former oil minister, said earlier this month Kurdish oil was expected to flow early next year. Al-Shahristani said the region could produce 150,000 bpd next year.
The dispute Iraqi Kurdistan and the central government over the contracts to develop the northern oil fields halted exports from the region last year.
Baghdad says contracts signed by the Kurdistan Regional Government with foreign firms to develop the oil fields in the north are illegal.
