"In February, we are going ahead of the schedule planned for this month," Novak told reporters.
He added that Russia planned to achieve the production levels envisaged by the agreement by the end of April.
OPEC's output cut deal was sealed on November 30, 2016, with members agreeing to cut oil output by 1.2 million barrels per day for the first six months of 2017. The total OPEC output has so far fallen by 890,000 barrel per day, according to its monthly report.
Eleven non-OPEC countries, including Russia, later joined the deal, pledging to reduce production by 558,000 barrels per day on a voluntary basis. Russian output fell by 120,000 barrel per day in January.