Measured in tonnes, average daily oil production stood at 1.548 million tonnes in that period, the source said, citing preliminary data that the Russian Energy Ministry obtains from oil companies.
The ministry, which is due to publish monthly production data for September on Oct. 2, did not immediately reply to a Reuters request for comment.
In August, Russia's oil output stood at 11.21 million bpd, virtually unchanged from July.
Russia appears to have increased oil production by more than 130,000 bpd in September compared with August levels, according to the preliminary data cited by the source.
Energy Minister Alexander Novak said earlier this month that oil production in September was expected to be higher than in August.
Last week, OPEC's leader Saudi Arabia and its biggest oil-producer ally outside the group, Russia, ruled out any immediate additional increase in crude output even though oil had reached $80 per barrel - a price considered too high by some producers and consumers.