Tens of thousands of people on Saturday filled an avenue in Moscow to protest against the alleged rigging of parliamentary polls in a new challenge to Russian strongman Vladimir Putin's authority.

Clutching white balloons and banners with the slogan "For Free Elections", the protesters thronged Sakharov Avenue in Moscow, symbolically named after the Nobel-winning dissident Andrei Sakharov who for years defied the USSR.

Police said 28,000 had already turned out for the Moscow rally but an AFP correspondent said the numbers could be as high as 40,000 with protesters filling Sakharov Avenue, which was closed off to traffic for the demonstration.

"We are here to show our anger. They (the authorities) install their own friends in power and they have split everything up between themselves. They are just like the Communists in the Soviet era," said protester Oleg Lefonov, 40.

Loudspeakers played the legendary song of Soviet rock musician Viktor Tsoi "We Want Change!". A banner held up by a group of protesters said: "We woke up and this is only the beginning."

Incensed by claims of wholesale violations in the polls that handed a reduced majority to prime minister Putin's United Russia, tens of thousands of people already took to the streets across Russia on December 10.

These protests are the biggest show of public anger in Russia since the chaotic 1990s and the first sign of a growing challenge to Putin's 12-year domination of the country.

The protests have put pressure on Putin to implement radical changes in Russia's tightly-controlled political system as he plans to return to the presidency in March elections after his four year stint as prime minister.

Around 100 people took part in a protest in the Far Eastern city of Vladivostok, an AFP correspondent said, and other rallies gathering up to 1,000 people took place in Siberia.

Former Russian finance minister Alexei Kudrin for the first time joined the opposition protest in Moscow and called for new elections to replace this month's disputed polls.

"We need to have early elections, adopt new laws about elections, and register those parties that were not registered," Kudrin, who held his post for over a decade before falling out with the Kremlin this year, told the Interfax news agency.

The Soviet Union's last leader Mikhail Gorbachev, 80, who has been virulently critical of the elections, had been considering attending but had not appeared so far.

Charismatic anti-Kremlin blogger Alexei Navalny was also expected to be present after his release from prison following a brief sentence for his participation in a protest shortly after the elections.

However the mass protests have been sanctioned by the authorities, in a major turnaround by the police who arrested hundreds of people who took part in demonstrations in the immediate aftermath of the elections.

President Dmitry Medvedev this week announced reforms to appease the proteseors -- including resuming elections for regional governors -- but the changes fell far short of their demands for a re-run of the legislative polls.

In an unexpected boost to the protesters, an advisory Kremlin rights panel said in a statement that the new parliament had been discredited by the accusations of fraud and fresh elections should be called.

"This discredits the electoral system and the lower house of parliament and... creates a real threat to the Russian state," it said in a statement, calling for the resignation of election commission chief Vladimir Churov.

It said that new election laws should be put in place "with the aim of then calling snap elections" to replace the current parliament.

But the commission dismissed the call for Churov to resign, with its member Yelena Dubrovina telling the Interfax news agency that "this decision does not have any legal, judicial consequences."

Defying the protests, the newly elected lower house of parliament, the State Duma, held its first session on Wednesday.

The ruling United Russia party won less than half the vote in the elections and lost 77 seats as fatigue set in with the rule of Putin, who is planning to win his old Kremlin job back in March polls and could stay in power until 2024.

But the opposition says the party's performance would have been even worse in free elections.