Russians are voting in an election that is likely to return Vladimir Putin for a fourth term as president.
Voting began in the Russian far-east at 20:00 GMT on Saturday, and opened in Moscow nine hours later. More than 100 million people are eligible to vote.
Exit polls are expected late on Sunday. Mr Putin is hoping for another six-year term and faces seven other candidates.
He said he would see as a success any result that gave him the “right to perform the duties of president.”
His comments were carried on national TV as he voted in Moscow.
Mr Putin’s rivals include a millionaire communist, Pavel Grudinin, a former reality television host, Ksenia Sobchak, and veteran nationalist Vladimir Zhirinovsky.
The main opposition leader, Alexei Navalny, has been prohibited from standing, because of a fraud conviction that he has condemned as politically motivated.
Mr Navalny has urged voters to boycott the election and has sent thousands of observers to polling stations to watch for possible violations.
Vladimir Putin, 65, has been Russia’s dominant leader since 1999, either as president or prime minister.
Election officials said that, as of 10:00 local time (07:00 GMT), turnout was 16.55%, much higher than in previous years.
They also said they had repelled a cyber attack on their website overnight. The distributed denial of service (DDoS) attack was sourced to 15 countries, they said.
A 100% turnout was reported in some areas of the far east. Interfax news agency quoted an election official as saying every resident in six villages on the Kamchatka peninsula had cast their ballots.
The same turnout was reported in four villages in the Chukotka region.
In some regions, free food and discounts in local shops were on offer.
Sunday’s vote is the first in Crimea since Russia seized the region from Ukraine.
The election falls on the fourth anniversary of a treaty, signed by President Putin, formally declaring Crimea part of Russia following its annexation.
The move was bitterly contested by Kiev and ratcheted up tensions between Russia and the West.
As a result, Russians living in Ukraine were unable to take part in Sunday’s vote because access to Russian diplomatic missions was blocked by the Kiev government.