The Central Election Commission said Communist party leader Gennady Zyuganov had received 19.73%, nationalist Vladimir Zhirinovsky - 12.47% and the leader of the tiny, pro-Western Democratic Party, Andrey Bogdanov - 1.53%.
Other exit polls gave Russian First Deputy Premier Medvedev, publicly-backed by current Russian President Vladimir Putin as his successor, some 70%. Putin has said he will take up Medvedev's offer to become president if his ally wins the election.
The Central Election Commission said turnout was 64.23% as of 7:00 p.m. Moscow time.
Gennady Zyuganov and Vladimir Zhirinovsky announced they would contest the results of the poll in court, citing voting violations.
Many Western observers, including the OSCE's main election arm, chose to boycott the election over restrictions imposed by Russia. Moscow rejected claims that it had imposed restrictions on monitors however.
Critics also pointed to pressure on voters, especially employees of state-run organizations.
