By Thomas Grove and Alissa de Carbonnel
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, while supporters of the prime minister staged a rival rally drawing comparable numbers.
Smaller protests were held in other cities across the vast country maintaining pressure on Putin one month before a March 4 presidential election he is expected to win. Putin's public image was shaken in December by allegations of fraud in parliamentary elections and protests unthinkable a year ago.
Their breath turning to white vapor clouds in the frigid Moscow air, tens of thousands of protesters marched within sight of the red-brick Kremlin walls and towers, chanting "Russia without Putin!" and "Give us back the elections!"
Putin was president from 2000 until 2008, when he ushered Dmitry Medevedev into the Kremlin because of a constitutional bar on three successive terms as head of state. Putin became prime minister but remained the dominant leader.
Putin presents himself as a man of action working for the good of the people and dismisses rivals as divided and lacking in any realistic policies to overcome the country's problems of industrial decay and poor transport and communications.
On Saturday, he was 1,500 km (900 miles) from Moscow, promising angry residents of the Ural Mountains town of Roza the state would move 3,800 people from homes threatened by shifting ground on the edge of the biggest open-pit coal mine in Eurasia.
"You see what we are doing, we are dealing with concrete problems of the people who live here," Putin said when asked about the demonstrations.
Saturday's 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, demonstrators bundled up against the cold marched down a broad central street, many wearing white ribbons symbols of protests whose main motto is "For Honest Elections." A digital clock flashed the temperature: minus 17 C (1 F).
"Not one vote for Putin!" Vladimir Ryzhkov, a liberal opposition leader, said to a roar of approval from the crowd at the rally that followed the march. Protesters packed a square across the river from the Kremlin, stamping and clapping to keep warm.
A patchwork alliance of disparate opposition leaders is 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.
Polls indicate Putin is all but certain to win the presidency despite a decline from previous popularity levels.
Opponents hope he will at least be forced into a runoff by falling short of a majority on March 4 and that persistent protests will undermine his authority, loosening his grip on power in a new six-year term and pushing him into concessions.
"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 120,000 people joined their protest in Moscow, which appeared smaller than that but as large as the December rallies that drew tens of thousands - suggesting their fears a cold snap might keep people away were unfounded.
Many protesters had banners making light of the bone-chilling weather and calling for Putin to go. "Down with the cold, down with Putin," one banner said. Others declared: "They froze our democracy" and "We are frozen in solidarity."
Police said 138,000 people attended the pro-Putin rally a few km (miles) away in Moscow, but reporters estimated the crowd was smaller than that by tens of thousands, and attendance at demonstrations in support of the former KGB spy has previously been swelled by the authorities ferrying in sympathizers by bus.
Teachers have said they came under pressure from trade unions to attend the pro-Putin rally.
"Trade union representatives called us together and said at least five to 10 people from each school had to go (to the Putin rally)," said Sergei Bebchuk, a 54-year-old headteacher who ignored the request and attended the opposition protest.
"I have something I believe in. We could not go there," he said, his daughter at his side with white ribbons in her hair.
Putin said Moscow's mayor had told him 190,000 attended the rally in his support there, and that while he did not rule out pressure had been applied, "to bring 134,000 or 190,000 people by applying pressure alone is impossible."
"It is totally obvious that people came to express their position. Their position is to support what we are doing. For me it is very important," Putin said. "I have said that I cannot work without it. I am really grateful."
At that pro-Putin rally, demonstrators carried posters saying "For Putin" with a check mark in a box next to his face. Another read "Putin led Russia out of civil war" and one said, "My children will live in Russia - I need Putin."
In keeping with Putin's warnings against revolutionary change and the anti-Western rhetoric he has employed in his campaign, the rally was billed as "anti-orange" - another reference to Ukraine, where Moscow has said Western-funded activists helped bring a pro-Western leader to power.
"My aim is to support the movement against the 'orange ones' - those America sends us to topple those in power and rock society," Kirill Domchenko, 25, a Moscow university student.
Putin in December accused the United States of encouraging opposition protests and said Western states were spending billions to influence Russian elections. He praised the 'anti-orange' demonstrators late on Friday and said "I share their views," Interfax reported.
The main opposition protests were suspended over the long New Year holiday, when Russia comes to a halt. Opposition activists 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, dismissal of the central election commission chief, the registration of more political parties and other political reforms.
The Kremlin has promised to let more parties contest elections but has rejected its main demands. Ryzhkov told the crowd protests must continue until Putin gives in, and another protest is planned for one week before the election.
Crowds of a few hundred turned out to protest against Putin in other cities across Russia, although the number protesting is still only a small part of the more than 140 million population.
In the Pacific port city of Vladivostok, demonstrators carried banners reading "Putin - out!" and "The crook is making for the throne again ... send him to a prison bunk."
The protesters are angered by allegations of fraud in a December 4 parliamentary election that was won by Putin's ruling United Russia party, albeit with a reduced majority in the lower house.
The plan by Putin and Medvedev to swap jobs after the presidential election is viewed by opposition supporters as openly flouting democracy.
"We are not sheep or cattle. We deserve respect," said Marat Yafyasov, 54, a lawyer who travelled from Yaroslavl, 250 km (155 miles) northeast of Moscow, to join the protest.
"We are out in the cold because we can't let this moment go, we have to keep the protest going."
(Additional reporting by Nastassia Astrasheuskaya in Moscow and Gleb Bryanski in Roza, Russia; Writing by Steve Gutterman; Editing by Timothy Heritage and Rosalind Russell)