By Steve Gutterman and Amie Ferris-Rotman
MOSCOW (Reuters) - Tens of thousands of people in Moscow and thousands more in cities across Russia demanded an end to Vladimir Putin's rule and a rerun of a parliamentary election on Saturday in the biggest opposition protests since he rose to power 12 years ago.
Potesters waved banners such as "The rats should go!" and "Swindlers and thieves - give us our elections back!" in cities from the Pacific port of Vladivostok in the east to Kaliningrad in the west, nearly 7,400 km (4,600 miles) away.
But the biggest protest by far was in Moscow, where riot police were out in force but just watched as protesters waving flags and shouting "Putin is a thief!" staged the opposition's biggest protest rally since the Soviet Union collapsed in 1991.
The protests showed a groundswell of anger over the December 4 election, which the opposition says was rigged to favor Putin's United Russia, and discontent with the prime minister three months before he tries to reclaim the presidency at the polls.
"Today 60,000, maybe 100,000 people, have come to this rally," former prime minister Mikhail Kasyanov said in a speech to a huge crowd packed into Bolotnaya Square across the Moscow River from the Kremlin.
"This means today is the beginning of the end for these thieving authorities," said Kasyanov, who now leads an opposition movement which was barred from the election.
People of all ages gathered in Moscow, many carrying white carnations as the symbol of their protest and some waving pictures of Putin and President Dmitry Medvedev declaring: "Guys, it's time to go." Helicopters at times buzzed overhead.
Vladimir Ryzhkov, an opposition leader, read out a list of demands including annulling the election and holding a new one, registering opposition parties, dismissing the election commission head and freeing people the protesters consider political prisoners.
"Russia has changed today -- the future has changed," he said, urging demonstrators to come out for new protests on December 24. The crowd chanted, "We'll be back!"
But Konstantin Kosachyov, a United Russia lawmaker authorized to speak on behalf of the Kremlin, ruled out negotiations on the organizers' demands and said: "With all respect for the people who came out to protest, they are not a political party."
The rallies, many of them held in freezing snow, were a test of the opposition's ability to turn public anger into a mass protest movement on the scale of the Arab Spring rebellions that brought down rulers in the Middle East and North Africa.
Most Russian political experts say the former KGB spy who has dominated the world's largest energy producer for 12 years is in little immediate danger of being toppled and that protests are hard to keep going across such a vast country.
But they say Putin's authority has been damaged and may gradually wane when he returns as president after the March election, unless he answers demands ranging from holding fair elections to tackling rampant corruption and reducing the huge gap between rich and poor.
"The time has come to throw off the chains," one of the main opposition figures, blogger Alexei Navalny, said in a message sent from jail following his arrest in a protest in Monday.
"We are not cattle or slaves. We have a voice and we have the strength to defend it," he said in the message, which drew cheers when it was read out from the stage by Oleg Kashin, an opposition journalist.
Such large protests were unthinkable before last Sunday's election, in which United Russia won only a slim majority in the State Duma lower house -- police warned protesters to get off a Moscow bridge at one point for fear it would collapse.
But in a sign that the Kremlin has started to sense the change of mood, most of Saturday's rallies were approved by city authorities hoping to avoid violence and state television showed footage of the protests - but no direct criticism of Putin.
PROTEST FROM EAST TO WEST OF RUSSIA
Invited by messages sent on social media, people protested in dozens of cities such as Vladivostok, Novosibirsk in Siberia, Arkhangelsk in the Arctic north, in Kaliningrad in the west, and in the Karelia region near Finland. Witnesses said 10,000 took part in a protest in St Petersburg, Russia's second city.
Police broke up an unapproved protest by about 400 people in Kurgan, on Russia's border with Kazakhstan, and at least 20 were detained in Khabarovsk near Russia's border with China, Russian news agencies said. Ten were held in St Petersburg, police said, and 35 were detained in Syktyvkar near the Arctic Circle.
"This is history in the making for Russia. The people are coming out to demand justice for the first time in two decades, justice in the elections," Anton, 41, a financial services sector employee who gave only his first name, said in Moscow.
"I want new elections, not a revolution," said Ernst Kryavitsky, 75, a retired electrician dressed in a long brown coat and hat against the falling snow in Moscow.
At least 100 trucks of riot police were parked near the Kremlin and columns of police trucks drove around the capital. Police put the number of protesters at around 25,000, and organizers said it was up to 150,000.
Medvedev has denied the allegations of fraud in the election. Putin, who became prime minister in 1999 and was elected president in 2000, has accused the United States of encouraging and financing the protesters.
The protesters were mainly angered by the election, in which they say only cheating prevented United Russia's result being worse. International monitors also said the ruling party had an unfair advantage and that they had evidence of ballot-stuffing.
Putin, 59, remains Russia's most popular leader in opinion polls, and has dominated the country under a political system in which power revolves around him. Far from all Russians wanted to take to the streets to protest.
"We think all these rallies, they're not right, because you need to work for justice in legal ways," said Lyudmila Mashenko, owner of a small business walking with her grandson in Moscow.
Some protesters want new elections but still back Putin.
"I came here today mainly to say that I don't agree with the result of election," the manager of an IT company in St Petersburg who gave her name only as Dasha.
But Putin has seen his support - won by restoring order after the chaos of the 1990s following the collapse of the Soviet Union - slip in opinion polls.
Many Russians felt disenfranchised in September when he and Medvedev announced plans to swap jobs after the presidential election and said they had taken the decision years ago.
(Additional reporting by Andrei Ostroukh, Thomas Grove and Guy Faulconbridge, Writing by Timothy Heritage, Editing by Steve Gutterman)