Former Soviet President Mikhail Gorbachev has said Sunday's Russian parliamentary election was marred by fraud and has called for a re-run.
"The country's leaders must admit there were numerous falsifications and rigging and the results do not reflect the people's will," he said.
Protesters were planning new rallies for Saturday as arrests in Tuesday's crackdown in reached 800 across Russia.
Key figures in the protest movement are starting 15-day jail sentences.
State TV channels have ignored the protests, giving coverage only to rallies in support of the government.
The centre of Moscow saw its biggest protest against the rule of Prime Minister Vladimir Putin and his allies in years on Monday, when several thousand people came out to condemn widely reported fraud at Sunday's parliamentary elections.
An attempt to hold a smaller rally on Tuesday was quickly broken up by riot police, while rival rallies by Putin supporters were allowed to proceed.
The big question now is whether the fledgling protest movement can maintain its momentum, the BBC's Daniel Sandford reports from Moscow.
While the movement began as a protest against the election results, most of the slogans have been against Mr Putin, our correspondent adds.
The Russian prime minister, who formally registered on Wednesday to stand in the March presidential election, has played down losses by his party, United Russia, which saw its support drop sharply to just under 50% of the vote.
OSCE monitors have said the polls were slanted in favour of United Russia, noting apparent manipulations such as the stuffing of ballot boxes.
Mr Gorbachev told Russian news agency Interfax in Moscow: "I think they [Russia's leaders] can only take one decision - annul the results of the election and hold a new one."
The former leader, 80, 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."
Messages on Twitter and other social media, used to co-ordinate the earlier protests, are fixing Saturday as the date for the next demonstrations.
Revolution Square, just 200m from the Kremlin, was named as the venue in Moscow.
Unconfirmed reports in the Russian media on Wednesday said the city authorities were planning to shut down the square's metro station of the same name "for repairs".
According to the Russian news website lenta.ru, the Solidarity opposition party has received permission from the city authorities to hold a rally on the square limited to 300 people.
However, the party's Facebook page "Rally For Honest Elections" had received nearly 16,000 requests to attend the rally as of Wednesday afternoon.
Plans are being discussed for rallies in 69 Russian towns and cities, from Saratov on the Volga to Krasnoyarsk in Siberia.
Nikita Batalov, a journalist for Russian commercial radio station Kommersant FM, has been blogging on his Twitter account about a pro-government rally on Wednesday on Moscow's Pushkin Square.
Quoting a mother, he said schoolchildren had been taken out of class and brought in for the event without parental consent.
Moscow police sources have told Russian media the number of arrests at Tuesday's opposition rally on Triumphal Square was 569, suggesting the gathering was much bigger than originally thought.
Many remained in custody on Wednesday morning, Russian media said.
Some 230 arrests were also reported in the second city, St Petersburg, and 25 in the southern city of Rostov-on-Don.
Veteran liberal politician Boris Nemtsov, who was detained at Tuesday's rally in Moscow, was freed after three hours in custody, he confirmed on his Twitter account.
Two key figures at Monday's rally, anti-corruption blogger Alexei Navalny and Solidarity activist Ilya Yashin, were both jailed for 15 days on charges of obstructing police.