Members of Russia’s Communist Party allege the vote was rigged after their defeat in races in the Russian capital.
A Russian opposition party has claimed that parliamentary election results from online voting were rigged.
The Communist party filed multiple lawsuits on Wednesday after their defeat in races in the Russian capital, Moscow.
The party finished second in the national polls in this month's election and had actively questioned the vote before polls opened.
Senior party members organised street protests and joined a coalition of Kremlin critics that is also attempting to annul the capital’s results from online balloting.
Russian election authorities have denied the accusations.
Voting online was available as an option at this month's election to Russian citizens in Moscow, as well as several other regions.
Election results made the Kremlin’s United Russia party the winner, and a supermajority with 324 of the 450 seats in parliament.
The Communist Party came in second with 57 seats — an increase from the 2016 election.
However, candidates put forward by the party lost races in 15 single-constituency districts in Moscow and blamed their defeat on the online balloting.
Critics pointed to a number of individual Moscow races as evidence of tampering, where Kremlin-backed candidates were losing until the results of online voting came in.
The Communist Party has refused to recognise the results of the vote in Moscow and staged two street protests, after which police detained several party members.
"From the tribune of the courtroom, we will spill light on all the methods that the authorities used to falsify the results of the election," said the party's senior member Valery Rashkin.
"This publicity, in front of the whole country and the whole world, terrifies them terribly," he told reporters outside a Moscow courthouse.
Also on Wednesday, the Communist Party’s faction in Moscow’s city Duma walked out of a session to protest the election results.
Rashkin, who was among those who lost individual races in Moscow at the last minute, said the party intends to fight until the end.
"We won’t be content with merely playing in court for a little and then stopping," he said.
"We have stepped on the path of battling for justice, for the truth, for elections that are fair, open, transparent, and competitive."