President Medvedev has promised to boost Russian democracy
Opposition parties in Russia have alleged that local elections across the country were marred by fraud.
Mayoral, regional and district council votes were held across Russia on Sunday, with some 30 million people eligible to vote.
Official results showed PM Vladimir Putin's United Russia party winning nearly every poll by a wide margin.
But opposition parties say they were refused registration to take part and were denied media access.
Votes were held in almost all regions, including Chechnya and Ingushetia.
As results came in on Monday, United Russia claimed victory after victory.
In the vote for Moscow City Council, election officials said United Russia won 66% and the Communists 13%. Those figures were expected to give the ruling party all but three of the 35 seats in the Moscow parliament, strengthening the hand of Moscow's powerful mayor, Yuri Luzhkov.
Opposition politician Boris Nemtsov has criticised the polls
The opposition liberal Yabloko party failed to win 5%, losing its place on the council.
The results, echoed across the country, wiped out opposition hopes that it could capitalise on the serious economic crisis in Russia, amid sharp negative growth and rising unemployment.
Instead, that inspired loyalty to United Russia, according to senior party official Boris Gryzlov.
"We can say that the voters and people of Russia, in a situation when we are fighting the global economic crisis, when we are struggling to stabilise the political situation, are with the party of power," he said.
Vladimir Churov, chairman of Russia's Central Election Commission, praised the electoral process.
"The elections were recognised [as] valid and were well organised, with a quite high turnout," he told Itar-Tass.
However, concerns over the polling led to one opposition leader, former Deputy Prime Minister Boris Nemtsov, calling on voters to boycott the elections or spoil their ballots.
"These elections are illegitimate. They're nothing but a farce," he told the Associated Press.
Mr Nemtsov was refused permission to stand in Moscow's city council election, AP reported, with election officials alleging the 5,000 signatures his party collected were forged.
Another opposition party, Yabloko, also alleged irregularities in Moscow, saying voters had contacted party officials to say they tried to vote but found votes already cast in their names.
Party observers also noticed large numbers of voters at a polling station who did not live in that voting area, Yabloko said, adding that it was preparing a complaint to election officials.