Vladimir Putin, the Russian president, in a televised address full of war symbolism has urged Russians to vote for constitutional amendments without mentioning that one of them would allow him to stay in power at least until 2036.
Election officials opened polling stations last week to avoid overcrowding outside voting booths that could lead to an increase in virus infections.
The Communist Party, which has advised supporters to vote "no" to the changes, complained of irregularities at two Moscow polling stations, where it said the number of registered home voters was 10 times higher than normal. Residents of Moscow and Niznny Novgorod have an opportunity to vote online.
Another Russian cosmonaut in orbit, Ivan Vagner, will vote on Wednesday via a proxy and a secure communications channel, the Russian space agency said.
Russian Federation is holding a referendum between June 25 and July 1 on a set of constitutional amendments, which, if passed, will enable Putin to participate in the 2024 presidential race.
The reforms also enshrine "faith in God" and Russian as the national language in the constitution, define marriage as between a man and a woman and ban giving away Russian territory or questioning the country's "historical truth".
"We'll fall ill and die - but we'll deliver the votes for Putin", joked allies of Kremlin critic Alexei Navalny, posting a video of a vote being held in a stairwell in Siberia near a flat where a coronavirus case had been registered.