Thousands of people have taken to the streets of Russia’s major cities to express their anger at over disputed parliamentary election results.

According to Russian authorities, 30,000 demonstrators took part in the rally in the capital. The BBC is reporting that the number was in excess of 50,000.

The demonstrators say that elections last Sunday, which resulted in a small victory for Putin's United Russia Party, were fraudulent. A smaller protest, of around 8,000 people, followed the December 5 vote, and there have been other, fragmented shows of opposition in the regions, analysts said.

In Moscow thousands of troops were deployed to maintain order. The demonstration, the biggest in Russia in twenty years, is the first ever challenge to Putin’s grip on power. The protesters are demanding that the elections be held again and the freeing of political prisoners.

The organisers of the protest in Moscow issued the following demands:

• Freedom for political prisoners
• Annulment of the election results
• The resignation of the election commission's Vladimir Churov and an investigation of vote fraud
• Registration of the opposition parties and new democratic legislation on parties and elections
• New democratic and open elections

The Kremlin originally sanctioned a protest of no more than 300 people to take place in Revolution Square. When the crowds far exceeded that number, the Kremlin compromised to allow 30,000 to congregate in Bolotnaya Square.

Away from Moscow, arrests were made in Russia’s second city St Petersburg, where the Guardian suggests around 7,000 gathered in opposition to Putin. The Associated Press is reporting that 100 arrests were made.

In total, demonstrations took place in around 80 cities across the vast country, with Reuters reporting protests from "Kaliningrad in the west to Vladivostok on the Pacific coast nearly 4,600 miles away."

Earlier, the Russian electoral commission has said there will be no fresh vote. Stanislav Vavilov, Vice chairman of the Central Election Commission, told the Interfax news agency that the “elections were acknowledged as valid and there are no reasons for any other opinions. We see no reason for election revision.”

According to the Telegraph, Russian state-controlled TV channels "confounded expectations of a media blackout and aired news pieces about today’s nationwide."

Following the demonstrations, Andrei Isayev, a top United Russia official, told CBC News that "expression of this point of view is extremely important and will be heard in the mass media, society and the state."

In London, a gathering of around 200 demonstrators protested outside parliament to support the action in Moscow and beyond.

Some commentators have been quick to associate the rising tide of opposition to Putin's administration with the Arab Spring of popular movements that deposed autocratic regimes in the Middle East and North Africa, although some analysts believe that Putin's grip on power is too strong.

Putin, now prime minister, served the maximum two consecutive terms as president before handing over to Dmitri Medvedev in 2008. He has indicated that he will run for president again in elections in March 2012.

"Russia is unlikely to follow the path of Egypt or other nations that comprise the Arab spring. Putin still retains significant popularity, and Russia has $515 billion in reserves of which approximately $115 billion could be used for social spending," Eurasia Group analyst Cliff Kupchan wrote on Friday night.

"Moscow's security forces remain loyal, and in a crunch, at least elite troops would probably use force. Many Moscow elites are disgruntled but garner significant benefits from the government, while among the population apathy is reduced but appears to remain widespread."

Perhaps more importantly, Russia's demographics show less strain - the country has no "youth bulge" of restive under-25s, who formed the core of the opposition to leaders in Egypt, Tunisia and Libya, and its unemployment rates are relatively low.

How the protests pan out is uncertain, analysts said, as the government has not been reticent to arrest en masse in the past. An escalation, either in Moscow or in the regions, could be worrying for Putin.

"Moscow insiders believe that a turnout of 50,000 or more nationwide is possible and would embolden protestors and give momentum to the movement," Kupchan said. "The size of turnout in the regions will be key; a large turnout would establish the protest trend on a national level. To date, the regions have been quiet on broad political issues, and Putin retains significant popularity in many of them. If excessive force is used, and casualties result, political strains could become severe."

On Friday, Putin moved to blame the unrest on outside agitation, with American and Hilary Clinton accused of sending “a signal” to “some actors in our country”.

Additional Reporting by Peter Guest.