Russians are voting in an election that is likely to return Vladimir Putin for a fourth term as president.
Polls closed in Moscow at 17:00 GMT, with final votes due to be cast an hour later in the far west of the country. More than 100m 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.
Independent election monitoring group Golos reported hundreds of irregularities throughout the day:
- Voting papers were found in some ballot boxes before polls opened
- Observers were barred from entering some polling stations
- Some people were bussed in amid suspicion of forced voting
- Webcams at polling stations were obstructed by balloons and other obstacles
In Dagestan, election official David Sepashvili says he was prevented from doing his job by some 50 "muscular men", according to AFP news agency.
"They filled the entire station, blocked the ballot box in a line," Mr Sepashvili, a member of the polling station's election commission, said.
The observer working at the station tried to reach the box to prevent ballot stuffing, but the men "knocked him on the ground, kicked him, and then carried him outside" before telling Mr Sepashvili to leave the premises.
"I went to the policeman at the station, but he said he can't do anything because he doesn't have a weapon," Mr Sepashvili said.
The election commission reported 13 breaches of electoral law and its head, Ella Pamfilova, said anyone involved in violations would be caught.
In some regions, free food and discounts in local shops were on offer.
Turnout a big issue for Putin
Analysis by Sarah Rainsford, BBC Moscow Correspondent
There's a lot to do besides vote at polling stations in Moscow today. We found a man playing The Clash on a balalaika outside one, and another man dressed as a rabbit.
There were competitions and games galore, and a giant sign for people to take selfies in front of, that reads: "I've elected the president."
It's all because turnout is the big issue at this election: Vladimir Putin wants the strongest possible mandate for another six years in power.
That's why the election was scheduled for 18 March - the anniversary of Russia's annexation of Crimea. Hugely controversial abroad, that act saw Mr Putin's political rating at home surge to its highest point ever.
Election officials said that by 18:00 Moscow time (15:00 GMT) turnout had reached almost 60%. They had earlier spoken of a "significantly higher" figure than in 2012. 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.
Russia's Tass news agency said that in Moscow, turnout was 59.5% an hour before polls closed there.
But opposition observers have said their estimates for turnout are significantly different form the official figures.
Sunday's vote is the first in Crimea since Russia seized the region from Ukraine.
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.