The movement against Vladimir Putin was on Sunday preparing new rallies to loosen the Russian strongman's 12-year grip on power after keeping up their challenge with a third mass demonstration in Moscow.

Tens of thousands marched through Moscow on Saturday despite bitterly cold weather to protest against Putin's domination, with organisers disputing police claims that a pro-Putin rally elsewhere in the capital was even larger.

Putin is still expected to win March 4 presidential elections where he is seeking a third Kremlin term after his four year stint as premier, but protest organisers emphasised that the polls mark only the start of their challenge.

The march on Bolotnaya Square over the Moscow river from the Kremlin was the third mass rally since fraud-tainted December 4 parliamentary elections sparked demonstrations that smashed the taboo against protests in Putin's Russia.

"We will come again," organisers wrote on their Facebook page Sunday morning under a picture of protestors sending hundreds of balloons into the Moscow winter sky.

One the chief organisers of the anti-Putin movement, politician Vladimir Ryzhkov, said he did not rule out holding a mass rally on February 26, one week before the polls, though most likely it would be a smaller 'flash mob' action.

"The big meeting is going to be on March 11 since, as far as I am aware, the extent of the fraud in the presidential elections is going to be huge."

Putin's biggest challenge in the elections is likely to come from Communist leader Gennady Zyuganov, who some analysts believe could push him to a second round but is an unpalatable figure for many in the protest movement.

Of the four candidates standing against Putin in the elections, only billionaire tycoon Mikhail Prokhorov attended the protest march and he did not give an address.

Founder of the liberal Yabloko party Grigory Yavlinsky, who was disqualified from taking part in the elections on procedural grounds, said in a rousing speech at the rally that 'life does not end on March 4 or even 5'.

"And perhaps our opponents and enemies will soon see and understand -- perhaps -- that everything is only just starting for us and for them it is ending," he said.

"We love our country and we will not give it up to thieves, fascists, Stalinists or other parasites."

Former cabinet minister turned bitter anti-Putin critic Boris Nemtsov hailed the success of the rally but warned three mass meetings were not enough to change the grip on power of Putin's circle.

"We are facing a prolonged, tough struggle with cynical and cruel swindlers and thieves. It is a marathon that we will certainly win," he said.

Police said that 36,000 attended the opposition meeting but Nemtsov and other anti-Putin leaders said over 100,000 had braved frigid winter temperatures of minus 17 degrees Celsius (1.4 degrees Fahrenheit).

By contrast, police said that 138,000 people had showed up for a pro-Putin rally in western Moscow, with Moscow deputy mayor Alexander Gorbenko saying the organisers should be fined for exceeding their planned turnout of 15,000.

But the opposition rubbished that turnout estimate and also said numbers were artificially boosted by employees of state companies being offered cash incentives or even being ordered to attend the pro-Putin rally.

Buses that had apparently been used to transport the pro-Putin demonstrators in from across the region surrounded the venue.

In comments Saturday evening, Putin acknowledged that 'administrative resources' could have been employed in mobilising supporters. He offered to personally help pay any fines the organisers might have incurred.