With cases surging and authorities urging Russians to stay in their homes, celebrations of this year's Victory Day were muted after the Kremlin grudgingly postponed plans for a grand parade with world leaders.

Instead of columns of military hardware and thousands of troops marching through Red Square as planned, Putin walked alone to lay flowers at the Eternal Flame outside the red brick walls of the Kremlin.

In a solemn televised speech, he made no mention of the virus, despite Russia having the fifth-highest number of confirmed infections in the world.

Putin instead highlighted the sacrifices made by the Soviet Union in what Russians call the Great Patriotic War and hinted at the threat now facing the country.

"Our veterans fought for life, against death. And we will always be equal to their unity and endurance," Putin said.

"We know and firmly believe that we are invincible when we stand together."

An honour guard marched past Putin after his speech, as Russian television showed images of Red Square empty under cloudy skies.

Military helicopters, bombers and fighter jets flew over the city, releasing smoke in the red, white and blue of the Russian flag.

State television counted down a minute of silence later in the evening, to commemorate the millions who perished in the war.