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 protestors thronged Sakharov Avenue in Moscow, symbolically named after the Nobel-winning dissident Andrei Sakharov who for years defied the USSR.

The police said 29,000 had turned out for the Moscow rally but organisers said 120,000 people had entirely filled to bursting point the Sakharov Avenue, which was closed off to traffic for the protest.

The protest increases the 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.

Some protestors held up pictures of Putin with a giant condom draped over his head in the style of an Egyptian pharaoh, in reference to his sneering dismissal of the rallies as resembling an anti-AIDS campaign.

In a hugely provocative speech, blogger Alexei Navalny who has emerged as one of the protest leaders, vowed that one million people would attend the next rally to demand new parliamentary elections.

"I see enough people here to take the White House (the seat of the Russian Government) right now. But we are peaceful people and we will not do that — for the moment," he said.

"We know what we will do. We will go out onto the street until they give back what is ours. Next time, we will bring one million people onto the streets of Moscow," he said to cheers.

"We do not want to scare anyone. But I promise you that next year the leaders will change and power will belong to those to whom it should belong. Power will belong to the people!"

Amid a festive atmosphere despite sub-zero temperatures, loudspeakers played the legendary song of Soviet rock musician Viktor Tsoi "We Want Change!".

A banner held up by a group of protestors 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.

"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 protestor Oleg Lefonov, 40.

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 warned that Russia risked a new revolution if there was no dialogue between protestors and the Kremlin.

"There needs to be a platform for dialogue, otherwise there will be a revolution and we lose the chance that we have today for a peaceful transformation" of Russia, he said.

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.

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 protestors — 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 protestors, an advisory Kremlin rights panel said overnight 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.

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.