Russia says its high number of cases is due in part to a massive testing campaign that has seen more than 6 million tests carried out.
Moscow accounts for roughly half of all infections and the city said it would be launching mass voluntary tests for antibodies from Friday.
Russian President Vladimir Putin this week announced that a nationwide lockdown aimed at slowing the spread of the virus would be eased, even as health officials record a steady increase in new cases.
Despite its high number of cases, Russia’s official coronavirus fatality rate is low in comparison to countries like the United States, Britain, Italy and Spain.
Authorities say this is because Russia was able to learn lessons from the experiences of western Europe, moving quickly to isolate travellers and people at risk, and launch a vast campaign to test and quarantine those infected.
But critics have cast doubt on the figures, accusing the authorities of under-counting by blaming virus-related deaths on other causes.
AFP contributed reporting to this article.