Daily figures released by health authorities showed Russia reaching 232,243 confirmed infections, behind only the United States which has reported more than 1.3 million.
Among the new infections was President Vladimir Putin's spokesman, Dmitry Peskov, who told Russian news agencies he had tested positive for the coronavirus and was being treated.
Officials say the high number of cases reflects a huge testing campaign, with some 5.8 million tests carried out so far, and point to the country's relatively low mortality rate as evidence Russia is managing the crisis.
Anxious to get the economy moving again, Mr Putin on Monday announced an end to a national "non-working" period in place since late March.
Over 10,000 new cases per day
Containment measures remained in many parts of the vast country, including hard-hit Moscow which is on lockdown until the end of May, but others began to lift some restrictions.
Officials reopened parks in Novosibirsk in Siberia and in Bashkortostan in the Urals and in Magadan in the Far East residents were allowed to leave their homes to exercise.
In Moscow some half a million construction and industrial workers were allowed back on the job, as wearing masks and gloves became mandatory in shops and on public transport.
Riding a bus in the capital, 25-year-old Tatyana Khan said it was clear why such measures were necessary.
"If everyone had worn masks earlier there probably would be fewer infections in Russia," said Ms Khan, who has been working for the city disinfecting building entrances.
After reporting more than 10,000 new cases per day for more than a week, Russia on Tuesday surpassed Britain and Spain in the total number of confirmed infections.
Russian Prime Minister Mikhail Mishustin (AAP) Source: Sputnik
But with only 2,116 virus deaths reported so far, Russia's mortality rate has been much lower in comparison with countries with similar infection rates.
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, convert hospitals to treating virus patients and launch a vast campaign to test and quarantine those infected.
Critics have cast doubt on the numbers, accusing officials of under-counting by blaming virus-related deaths on other causes.
The Kremlin has left it up to individual regions to decide how to proceed with easing restrictions. In Moscow residents will still only be allowed to leave their homes for brief trips or to travel to work with a permit.
Young people hold hands as they walk in central Moscow (AAP) Source: Valery Sharifulin/TASS/Sipa USA
Medical workers have warned that despite the increase in capacity, hospitals and clinics have been stretched in dealing with the crisis.
On Tuesday officials launched a probe into ventilators used at some Russian medical facilities after five coronavirus patients, including three attached to the breathing machines, died in a fire at a Saint Petersburg hospital.
Saint Petersburg governor Alexander Beglov said it appeared that one of the ventilators at the Saint George hospital had short-circuited and caught fire.
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