By Alissa de Carbonnel and Thomas Grove
MOSCOW (Reuters) - Tens of thousands of Russians defied bitter cold in Moscow on Saturday to demand fair elections in a march against Vladimir Putin's 12-year rule, and thousands of others staged a rally supporting the prime minister.
Opposition protesters also organized smaller protests in other cities across the vast country, one month before the March 4 presidential election which Putin is expected to win.
Putin was president from 2000 until 2008, when he ushered Medevedev into the Kremlin because of a constitutional ban on three successive terms as head of state. Putin became prime minister but remained the dominant leader.
Temperatures far below freezing tested the power and perseverance of a street protest movement fuelled by suspicions of fraud in a December parliamentary election and dismay among some Russians over Putin's plan to rule at least six more years.
In the capital, thousands of demonstrators bundled up against the cold marched down a broad central street, many wearing white ribbons that have become symbols of protests. A digital clock flashed the midday temperature: minus 17 C (1 F).
Opposition leaders are trying to maintain momentum after tens of thousands turned out on December 10 and December 24 for the biggest opposition protests since Putin was first elected president in 2000.
"We have already reached a point of no return. People have stopped being afraid and see how strong they are together," said Ivan Kositsky, 49. He said Putin "wants stability, but you can only find stability in the graveyard."
Kositsky wore an orange ribbon in a reference to the 2004 Orange Revolution in Ukraine, where peaceful protests following allegations of widespread election fraud helped usher an opposition candidate to the presidency.
Opposition leaders said up to 100,000 people had joined their protest in Moscow and reporters said there appeared to be no fewer protestester than at the last big opposition protests in December.
Police said up to 90,000 people were at the pro-Putin rally a few miles (kilometers) away in Moscow although attendance at demonstrations in support of the former KGB spy have previously been swelled by the authorities ferrying in sympathizers by bus.
Teachers have said they came under pressure to attend the pro-Putin rally from trade unions.
"Trade union representatives called us together and said at least five to 10 people from had to go to the Putin rally," said Sergei Bedchuk, a 54-year-old headteacher at the opposition protest in Moscow.
"I have something I believe in. We could not go there," he said, his daughter at his side with white ribbons in her hair - the symbol of the protest movement.
The main opposition protests were suspended over the long New Year holiday, when Russia comes to a halt and had been concerned that the protests might lose momentum after Putin, 59, ignored all their main demands.
The protesters want a rerun of the parliamentary election, the release of prisoners jailed for political reasons, reform of the political system, dismissal of the central election commission chief and registration of more political parties.
A key demand has been added for sympathisers not to cast a single vote for Putin on March 4.
(Writing by Steve Gutterman, Editing by Timothy Heritage)