Russia registered a record number of new coronavirus infections on Monday with cases in Moscow surpassing a previous high set in May.

The Kremlin has so far ruled out putting back into place sweeping restrictions that were lifted earlier this year, despite weeks of rising cases in Russia.

An official coronavirus tally on Monday said new infections reached 21,798, nearly doubling the country's first-wave record in May.

Kremlin spokesman Dmitry Peskov conceded that the steady growth in cases in Russia "remained alarming", but noted that "not all countries are in lockdown".

Russia, the fifth worst-hit country in the world after the United States, India, Brazil and France, has recorded a total of 1,796,132 infections.

Unlike several European countries which have reimposed quarantine regimes after suffering spiralling infections, hospital admissions and deaths, Russia has yet to announce plans for sweeping anti-virus measures.

In Moscow, the epicentre of the outbreak, new infections reached 6,897 on Monday, surpassing the May record by more than 100. There were also 256 new deaths nationwide, bringing the total to 30,793.

Russia has reported a much lower virus fatality rate compared to other badly hit countries and Kremlin critics have accused the government of attempting to downplay the severity of the pandemic.

The government recently announced an aid package worth 11 billion rubles ($138.6 million) for regions which have struggled to manage a rapid surge in cases.