Officials reported that 20% of new cases were asymptomatic. The country's confirmed coronavirus case total now stands at 647,849.
Russia's fresh infections count has maintained below 7,000 for five days in a row.
The updated statistics include 154 new fatalities recorded over the past 24 hours. The country's overall death toll is now 9,320 – a rate much lower than in other countries with similar outbreaks of the disease.
Russian officials have attributed the low count to mass testing, while critics have accused the government of deliberately underreporting the figures in order to downplay the severity of the crisis.
9,220 people recovered over the past 24 hours, bringing the overall number of recoveries to 412,650.
225,879 COVID-19 cases remain active.
The majority of new infections (745) were reported in Moscow – it remains the country's most-affected area in terms of total confirmed cases, with 221,598, 67,405 of which are active.
The Moscow region reported the second-largest increase in infections (301 new cases; 57,570 total), followed by the Khanty-Mansi Autonomous region (279 new cases; 8,958 total) and the Sverdlovsk region (276 new cases; 12,792 total).
Russia's highest one-day coronavirus tally – 11,656 cases – was posted on May 11. The country is in third place worldwide in terms of total confirmed COVID-19 infections – the US is in first with over 2.59 million cases, while Brazil is in second with over 1.36 million.
Multiple regions, including Moscow, have been rolling back quarantine measures to accommodate Russia's plebiscite on amendments to the Constitution, scheduled to run from June 25 to July 1. If the majority of Russians vote in favor of the amendments, Vladimir Putin's presidential term clock will be reset, allowing him to stay in power until 2036.
As of 10.00 GMT on June 30, there are over 10.3 million confirmed COVID-19 cases worldwide, according to Johns Hopkins University's latest data. The virus has claimed the lives of over 505,500 people. Over 5.23 million patients have recovered.