This compared with a previous record high of 10.30 million bpd hit in September.
Russia has kept ahead of Saudi Arabia as the world's largest crude producer. Last month the kingdom's output declined to 9.4 million bpd from 9.6 million bpd, according to a Reuters survey.
October was the first month of the new "60-66" taxation regime for the Russian oil industry, which cut duties on crude and some refined products to stimulate output of high-grade oil products and crude oil.
Hydrocarbons are a major source of state revenue, which must be replenished after an increase in spending ahead of parliamentary elections in December and a presidential vote in March.
Reuters reported overall daily natural gas production increased 13% to 1.8 billion cubic metres last month from 1.59 Bcm in September. Gas output at the world's largest natural gas producer, Gazprom, rose 15% to 1.35 Bcm a day.