In the last 24 hours the country has reported 10,899 infections, the tenth consecutive day that number has been above 10,000.
Among the infected is President Vladimir Putin's spokesman Dmitry Peskov, local media report.
He is the latest high profile official to test positive, after Prime Minister Mikhail Mishustin caught the illness.
The news comes the day after President Putin eased the country's lockdown. Factory and construction workers returned to work on Tuesday, though Mr Putin gave regions freedom to set restrictions depending on local circumstances.
Despite the high number of confirmed cases, Russia's death toll is only 2,116.
Government officials say the country's mass testing programme is responsible for that low mortality rate, but many believe the number is in fact far higher.
Meanwhile, authorities in St Petersburg have put out a fire in an intensive care unit, which killed five coronavirus patients and forced the evacuation of about 150 people.