New infections have been steadily dropping since mid-May when officials were reporting daily increases of around 11,000 cases.
Officials say Russia’s high virus count is the result of mass testing and that a steady decline in new infections and its low fatality numbers mean the country can begin to return to normal.
Yet critics have cast doubt on the numbers, accusing the authorities of under-reporting deaths and threatening a new wave of infections by lifting restrictions.
Russian President Vladimir Putin on Monday announced that a postponed nationwide vote on constitutional reforms that could extend his hold over power will go ahead on July 1.
The authorities have also rescheduled Russia’s massive May 9 Victory Day military parade for June 24.
Moscow, the epicenter of Russia’s pandemic with around half of the country’s total cases, on Monday eased a nine-week lockdown allowing shops to reopen and residents to leave their homes for short walks.
Putin was scheduled to meet with Prime Minister Mikhail Mishustin on Tuesday to discuss proposals to restart an economy badly hit by lockdown measures and a sharp fall in oil prices.
AFP contributed reporting to this article.