Over 50,000 people rallied Saturday in Moscow while thousands more came out across Russia following disputed polls in the biggest ever national show of defiance against strongman Vladimir Putin's 12-year rule.

A crowd chanting "Russia without Putin" marched past tight police cordons to a square on an island in the Moscow river amid anger at alleged vote-rigging in December 4 parliamentary elections won by Vladimir Putin's ruling party.

The polls were seen as a test of Putin's decision to return to the Kremlin for up to 12 more years via a job swap with Medvedev.

Similar scenes were replayed on a smaller scale in the Far East and across the industrial hubs of Siberia and the Urals -- a sign that Putin's path back to the Kremlin in March polls may be more fraught than it appeared just a week ago.

"Right now there is actually a chance for us to change something in this country," said 44-year-old Anna Bekhmentova as the demonstrators chanted "No to a police state!" and tied the protest movement's white ribbons to their winter jackets.

"No-one I know voted for United Russia," said Bekhmentova in reference to a party the opposition has branded a gang of "swindlers and thieves."

The biggest show of public anger in Moscow since the turbulent 1990s brought police helicopters out overhead and more than 50,000 officers onto the streets just six days after United Russia clung onto power with the alleged help of fraud.

But fury over the ballot and signs of sudden Kremlin weakness have stirred many to call not only for a new election but also an end to the stage-managed politics ex-KGB agent Putin introduced on his sudden rise to power in 2000.

"People who have connections to the authorities feel like they can do anything," said 26-year-old lawyer Yelizaveta Derenkovskaya. "I came to support people who want to change this system."

Police put the turnout figure at 25,000 for Moscow and detaining 30 during a 10,000-strong rally in Saint Petersburg where both Putin and President Dmitry Medvedev grew up.

But organisers and opposition lawmakers estimated the Moscow gathering at 50,000-80,000 -- with some saying more than 100,000 had come out in a display of people's power never before seen in the Putin era.

They also called for repeat demonstrations on December 24 should the poll results not annulled.

"This is probably the last chance we get of changing anything," said 23-year-old Ilya Sarmabarov as he held up signs with others on Saint Petersburg's Pionerskaya Ploshad square.

The rolling rallies kicked off in Far Eastern hubs such as Khabarovsk where around 40 people were detained during an unsanctioned rally attended by some 400 people in minus 15 degree Celsius (five degrees Fahrenheit) chills.

Organisers also reported 5,000 showing up in the struggling industrial town of Chelyabinsk and up to 4,000 in nearby Urals Mountains city of Yekaterinburg while similar rallies were also reported in Western Siberia and the south.

State television -- an object of scorn for much of the Russian Internet community for its blanket ban on coverage of post-election unrest -- took the unusual step Saturday evening of leading its news programme with Moscow rally coverage.

Some in the Russian opposition interpreted this as an early sign of change while a Kremlin source told the popular gazeta.ru news site that the decision to run the mostly-balanced reports was taken personally by Medvedev.

The Kremlin source added that Medvedev had also instructed the Moscow police to handle the protesters "extremely gently" after seeing more than 1,600 activists bundled away by riot police the previous week.

Putin's spokesman Dmitry Peskov said the Russian premier had no immediate comment.

Analysts say rapid social change and the Internet's growing penetration in Russia may have caught Kremlin strategists off guard.

A running public opinion poll conducted by the independent Levada Centre showed Putin's ratings taking a dive immediately after he announced his presidential ambitions on September 24.

The opposition to Putin is also expanding beyond a narrow base of veteran liberals and far-right nationalists to attract popular cultural figures with broad appeal such as detective story writer Boris Akunin.

"I have not seen Moscow like this for 20 years," Akunin told the Moscow crowd from the stage before adding that it was his first speaking appearance at a rally of any kind.