Of the 601 new cases, 448 are in Moscow, 34 in Moscow region.
"Four patients with coronavirus have died in a day: two in the Komi Republic, one in Moscow, and one in Perm Territory. The total number: 34," the response centre said.
Four people who tested positive for coronavirus have died in the last 24 hours, bringing the total to 34.
Forty-six people have been discharged from the hospital, bringing the total number of recoveries to 281.
Almost 50% of new coronavirus patients in Moscow are younger than 45, according to the response centre.
Earlier, Russian President Vladimir Putin has extended the nationwide paid holiday, which was to last a week starting 30 March, until the end of April. Separately, Moscow Mayor Sergei Sobyanin prolonged the quarantine in the capital until 1 May.