A spokesman for the Russian Prime Minister, Vladimir Putin, has said that the majority of Russians support him.
The announcement was issued after tens of thousands of people turned out in Moscow yesterday to demand a re-run of the parliamentary elections, which they say were rigged.
Organisers said 120,000 people attended the extraordinary rally where protesters chanted anti-Putin slogans.
Police put the numbers at 29,000 but AFP correspondents said the turnout was clearly bigger than the first rally two weeks ago which smashed the taboo in Russia against mass opposition protests.
The last Soviet leader Mikhail Gorbachev also dramatically called on Mr Putin to quit, just as he had done on 25 December 1991 when the USSR collapsed exactly two decades ago.
"This is not an outburst which will die down. This is not about the protests but about the mood," Yevgeny Gontmakher, head of the Centre for Social Policies at the Moscow-based Economics Institute, told AFP.
"There is a danger of a revolution. Authorities are making concessions but are not keeping up with the development of the events."
Russia's state television took the surprise decision to cover the rally hinting at an easing of a long-held taboo against direct criticism of Mr Putin, who came to power 12 years ago and wants to stay at the helm until 2024.
"Sharply negative appraisals of Vladimir Putin have been voiced several times," said a report about the rally broadcast on the Channel One on Saturday night.
With opposition supporters stepping up their challenge to Mr Putin in a campaign first triggered by claims of fraud in the parliamentary polls, a growing public anger against Mr Putin has become impossible to ignore.
"Channel One honestly speaks of the anti-Putin nature of today's meeting. That obviously cannot be pure coincidence," said Vladimir Varfolomeyev, a commentator with liberal Echo of Moscow radio.
Mr Putin - who announced a plan to leave his current post as prime minister to reclaim his old Kremlin job in March presidential polls - is struggling with the worst legitimacy crisis of his rule.
Mass protests were triggered by widespread claim of wholesale violations in the parliamentary polls this month which handed a reduced majority to Putin's ruling United Russia party.
Protesters called for the annulment of the ballot, sacking of the Central Election Commission chief and a re-run of elections.
Hoping to ride out a wave of protests, Mr Putin ignored those demands and promised instead a return to direct election of governors and a simplified procedure to register political parties.
In defiance of protests, the newly-elected lower house of parliament convened for its first session earlier this week.
Incensed by the Russian premier's claims that opposition supporters were in the pay of the US State Department and insults comparing them to an anti-AIDS campaign, protesters are now taking their anger out directly at Mr Putin.
The protest movement - which brings together a charismatic anti-corruption blogger, a detective story writer, musicians and a former finance minister - does not so far have a clear leader but is gaining momentum.
The blogger, 35-year-old Alexei Navalny, vowed that 1 million people would attend the next anti-Putin rally but the opposition has yet to announce when this will happen.
