MOSCOW - Tens of thousands took to the streets of Moscow Saturday for rival rallies duelling over Russia's future, in a test of strength for the anti-Vladimir Putin movement one month before presidential polls.

Bundled up in down jackets, fur coats and felt boots, the demonstrators defied freezing weather of around minus 17 degrees Celsius (1.5 Fahrenheit) as Russia's political temperature heated up ahead of the March 4 elections.

As protesters from the opposition movement massed for their third rally in less than two months urging the Russian strongman to quit, Putin's supporters also filled a square in western Moscow to bursting point.

Police said 138,000 turned up for the pro-Putin rally in the west of the capital but an AFP correspondent at the scene said the numbers appeared to have been exaggerated, amid allegations that people had been induced or pressured to attend.

Police put the number of protesters at the anti-Putin event called through social networks at around 36,000.

But the organisers of the anti-Putin rally -- its third since fraud-tainted December elections -- said some 120,000 people turned up, repeating the success of the previous demonstration despite the harsh temperatures.

"When people come out in such freezing cold, even more than 100,000 people, it means they are so sick of it that they do not have the patience to bear it any longer," opposition politician Boris Nemtsov said.

Putin is standing for a new term as president in the elections after his-four year stint as prime minister and his main opposition will come from the Communists.

"We are not afraid of the frost. We are afraid of lies," said Mikhail Matrosov, a 51-year-old businessman. "We are for fair elections."

The protesters massed in Bolotnaya Square just across the Moscow river from the Kremlin to hear speeches from activists and politicians calling on Putin to quit for the sake of the country.

"Putin wants to rule forever! One, two, three: Putin leave!" cried activist Ilya Yashin as the crowd roared back its approval, while leftist activist Sergei Udaltsov tore up a portrait of the Russian strongman on stage.

The leader of the liberal Yabloko party, Grigory Yavlinsky, said: "We are different but we are all of the same colour, the colours of the Russian flag!"