RIA Novosti reported Sunday with 20 percent of the ballots counted, Medvedev had nearly 65 percent of the vote, according to Central Election Commission data.
Exit polling had indicated Communist party leader Gennady Zyuganov had 19.73 percent support, nationalist Vladimir Zhirinovsky had 12.47 percent and the leader of the Democratic Party Andrey Bogdanov had 1.53 percent of the vote.
Zyuganov and Zhirinovsky said they planned to contest the election in court.
Medvedev, 42, is Russian first deputy prime minister and heads the Russian gas monopoly Gazprom. He was endorsed by current Russian President Vladimir Putin.
Election officials say pegged voter turnout at about 64 percent as of 7 p.m. Moscow time.
Critics have charged that voter turnout figures might have been inflated by the Kremlin to avoid embarrassment, Deustch Welle said.
The Parliamentary Assembly of the Council of Europe, one of the few international vote-observers monitoring the election said the election "could hardly be considered fair," the German newspaper reported.
"The violations have started already," said Liliya Shibanova, director of Golos, Russia's top independent elections monitoring body.
The parliamentary assembly boycotted the election, objecting to restrictions imposed by Moscow.
Notable deaths of 2014 [PHOTOS]