Former Soviet President Mikhail Gorbachev says Russia should annul the results of Sunday's parliamentary election and re-run the vote. He says the result do not reflect the will of the people.
The election was won Prime Minister Vladimir Putin's United Russia party by a slim majority, but there are claims of widespread fraud.
Police have arrested as many as 1000 protesters since Sunday.
State television channels have ignored the protests, giving coverage only to rallies in support of the government.
The biggest demonstration was in the centre of Moscow on Monday. An attempt to hold a smaller rally on Tuesday was quickly broken up by riot police.
The BBC reports Mr Putin has played down the losses by his party which saw its support drop sharply to just under 50% of the vote.
Mr Gorbachev, 80, told the Interfax news agency in Moscow: ''I think they (Russia's leaders) can only take one decision - annul the results of the election and hold a new one."
Mr Gorbachev initiated democratic reforms in the final years of the USSR but rapidly lost popularity and influence after the emergence of the new Russian state under the late Boris Yeltsin.
''Literally by the day, the number of Russians who do not believe that the declared election results were honest is increasing,'' he said.
''In my opinion, disregard for public opinion is discrediting the authorities and destabilising the situation.''
Mr Gorbachev has criticised Mr Putin in the past. He is admired in the West, but commands little respect among ordinary Russians.
Meanwhile, messages on social media are fixing Saturday as the date for the next demonstrations in Revolution Square, 200 metres from the Kremlin.