This is still below June's average of 11.15 million bpd and lower than Russia has commited to reduce under a global deal.
Russian oil production fell close to a three-year low in early July, as output was undermined by a row between Russian oil pipeline monopoly Transneft and the country's biggest producer Rosneft.
Transneft curbed oil intake from Yuganskneftegaz, Rosneft's main upstream unit, the oil producer said, hurting production that has already been depressed by an oil contamination crisis.
Last week, Russian Energy Minister Alexander Novak said there were no curbs at Yuganskneftegaz and that Russian oil production was back to level, stipulated in the global oil deal with OPEC.
The sources said that output at Yuganskneftegaz was still down in July 1-21 by 11pc from June's average, while Rosneft's total production, excluding joint ventures, declined by 4 percent for the period.
Rosneft, Transneft and the energy ministry did not immediately reply to requests for comment.
Russia has agreed to reduce its oil production by 228,000 barrels per day (bpd) from the 11.41 million bpd it pumped in October 2018, the baseline for the current global deal.
Under that formula, its output should be around 11.17 million-11.18 million bpd. Industry sources said oil output fell to 10.79 million barrels per day (bpd) in early July.