•The official vote is scheduled for 1 July, but authorities said they were opening polling stations a week early to stop overcrowding amid the pandemic.
•Opposition activist Alexei Navalny has said the changes will allow Mr Putin to be "president for life".
Russia has begun voting on constitutional reforms that could allow President Vladimir Putin to serve another two terms in office.
The official vote is scheduled for 1 July, but authorities said they were opening polling stations a week early to stop overcrowding amid the pandemic.
Opposition activist Alexei Navalny has said the changes will allow Mr Putin to be "president for life".
Mr Putin, however, has said they will ensure Russia's stability.
Although the president has not publicly said he would run again in 2024 when his current term ends, he has said it is vital he has the option.
"Otherwise I know that in two years, instead of working normally at all levels of the state, all eyes will be on the search for potential successors," he said in an interview earlier this week.
What are people voting on?
The big changes would limit a president's rule to two six-year terms in total, rather than two consecutive terms, and reset the clock so Mr Putin could continue in office after 2024.
Aside from potentially allowing him to lead Russia until 2036 - the reforms would give the president power to nominate top judges and prosecutors for approval by Russia's upper house of parliament.
They would also entrench conservative measures in the constitution, including an effective ban on gay marriage and an affirmation of Russia's "faith in God".
And economic changes would also be enshrined, including on the minimum wage and adjusting the state pension in line with inflation.
Roughly 110 million voters from Kaliningrad on the Baltic coast to Kamchatka on the Pacific are eligible to vote. Officials are providing masks and hand sanitiser at polling stations across the country.
The BBC's Sarah Rainsford in Moscow says a big turnout is vital for the Kremlin.
Officials have confirmed that people with Russian passports in separatist-controlled eastern Ukraine will also be allowed to take part. Last year, President Putin made it easier for residents to get Russian passports and officials estimate some 150,000 people in the rebel-held areas of Luhansk and Donetsk could take part.
What do critics say?
Mr Navalny, a figurehead of Russia's opposition, has called the vote a "coup" and a "violation of the constitution". Some argue Mr Putin is trying to cling to power, or give himself an option to stay on if he cannot find a suitable successor.
The 67-year-old former KGB agent has led Russia for 20 years, both as president and prime minister. But his popularity levels have dropped in recent years thanks to economic struggles and deeply controversial reforms to the pension system.
Mr Putin introduced the reforms to Russia's 1993 constitution in January, and they have already been adopted in both the houses of parliament in Moscow. But the president said a public vote would give the changes legitimacy, and initially scheduled the poll for April before delaying it due to the coronavirus outbreak.
Activists organised marches to oppose the vote the same month but authorities banned them, citing rules about public gatherings amid the coronavirus lockdown. A website set up to collect signatures of people opposed to the vote was shut down by the courts.
Senior politicians around the country have come out in favour of the changes, and observers believe there is little doubt the measure will pass. Copies of the new constitution are already on sale in Russian bookshops.
Many have questioned the timing of Russia's World War Two Victory Parade. Tens of thousands of troops marched through Moscow on Wednesday - despite a ban on mass gatherings under lockdown rules - just a day before voting began.
What about the coronavirus?
The pandemic has further dented Mr Putin's standing.
Russia has the third-highest number of recorded infections worldwide, with 613,994 confirmed cases and 8,605 deaths - although critics believe the true death toll is far higher.
Latest figures released on Thursday showed there were 7,113 new cases reported over the last 24 hours. In May, Russia reported more than 10,000 new cases a day for more than a week.