Opposition parties say the poll will not be free and fair.
Backed by president Putin, United Russia usually labels itself as a centrist party and was founded in April 2001.
It has been making gains in recent federal and local elections due to the popularity of Putin – although he is a non-member.
Putin announced on October 1 that he would head party's list for elections on December 2, guaranteeing him a place in the Duma - Russia's lower house of parliament.
has cast the election as a referendum on his rule, saying that a vote for United Russia would safeguard the country's oil-driven economic boom and stability.
"The result of the parliamentary elections will, without a doubt, set the tone for the elections for a new president," Putin said in a televised address aired for a second time on Friday.
In his final pitch to voters, Putin urged them to turn out, claiming that a vote for his opponents could return the country to the "humiliation, dependency and disintegration" of the early post-Soviet years.
As required by law, a campaign blackout went started at midnight on Friday, although United Russia posters remained in the capital, Moscow, while those of the 10 other parties were less visible.
The opposition has accused the Kremlin of suppressing debate during the campaign by dominating coverage on state-run TV, confiscating their election leaflets and arresting members.
Garry Kasparov, a critic of the Kremlin, has dismissed the elections as a "farce" and warned that Putin is leading the country towards dictatorship.
After being detained for five days this week for taking part in an unauthorised protest against Putin, Kasparov accused the president of resorting to repression to cement his party's dominance.
|Putin says a United Russia victory will safeguard Russia's oil-driven boom|
"Fear is the only chance this regime has to survive," Kasparov said.
The Russian authorities and businesses are trying to maximise the turnout by encouraging mobile phone subscribers to vote.
Election monitors say they are concerned by allegations that voters are being pressured by the authorities to vote at their workplaces, under the supervision of their bosses.
About 450,000 police officers will be on duty on Sunday, and 95,000 polling stations have been set up across Russia's 11 time zones.
Voting starts at 8am (2000 GMT) on Saturday in the far east region of Kamchatka and ends on Sunday at 6pm (1800 GMT) in Kaliningrad.
The campaign for the presidency started on Wednesday with no clear frontrunner. Candidates must register by December 23.