The center reported 269 deaths in the past 24 hours, and added that the current growth rate in the infections is 1.2%.
It said the number of new cases in Moscow -- Russia's most affected city -- had decreased slightly, falling below 5,000 for the first time in days.
The total number of reported coronavirus cases in Russia as of October 20 is 1,431,635. It has reported 24,635 deaths, although the real figure is likely to be higher, due to the way the country calculates deaths, and reports of high excess mortality this year.