Russian President Vladimir Putin ordered the government to provide daily forecasts of the spread of the novel coronavirus as Russia recorded almost 5,000 new cases in a single day.
Coronavirus infections in Russia began rising sharply in April after reporting far fewer infections than many western European countries in the outbreak's early stages.
On Saturday, Russia's official tally of coronavirus cases was 36,793, a record overnight rise of 4,785, and death toll rose by 40 to 313.
The government must "provide a short-term prognosis of the number of citizens who may contract the new infectious disease (COVID-19)" and report its estimates on a daily basis, according to an order published on the Kremlin's website.
In Moscow, a city of 12.7 million people which became the epicentre of Russia's coronavirus outbreak, cases jumped by 2,649 to 20,754, and the capital city accounted for half of all new fatalities reported on Saturday.
However, Moscow mayor Sergei Sobyanin said the lockdown measures first introduced in March were bearing fruit.
"The disease rate in the city is growing but not exponentially, and far from the worst-case scenario," Sobyanin wrote on his website.
"A week ago, Moscow medical institutions were working at their limit. Today, they have switched to a more normal mode with a good stock of capacity," Sobyanin said.
Initially declared on March 30, the lockdown regime banned residents from leaving their homes unless they were going to buy food or medicines, get urgent medical treatment or walk the dog.
The authorities also introduced a travel permit system effective from April 15, and Sobyanin said on Saturday the authorities would use traffic cameras to catch drivers travelling without passes.
Authorities and clerics have urged Christians to stay home during the Orthodox Easter weekend, although a senior cleric urged police on Saturday to be lenient on those who still try to make it to their church.