Vladimir Putin's United Russia party has won nearly 80% of the seats in local and regional elections held yesterday.
The elections were held in 75 regions of the country.
The Liberal Yabloko party contest the results saying that it had received a 'storm of calls' from Moscow voters who said they were unable to vote at polling stations because someone else had already voted in their name.
Both the Yabloko party and the Communist Party said they would question the election results in court.
United Russia won 107 out of 135 seats in regional legislatures and 189 out of 235 seats in municipal legislatures, according to Russian news agencies.
In Moscow city, United Russia and the main opposition Communist Party were the only parties to win seats, while the liberal Yabloko party was squeezed out.
Turnout was just under 35% in the Russian capital, according to news agencies.
99% of the ballots are counted in the Moscow election, with United Russia having achieved 66% of the vote, the Communists have 13% while other parties have failed to pass the 7% barrier they had needed to win seats.
Final results for all the elections are to be published later this week.