Tens of thousands of people have gathered in central Moscow in a show of anger at alleged electoral fraud.
Protest leader Alexei Navalny told the crowd to loud applause that Russians would no longer tolerate corruption.
“I see enough people here to take the Kremlin and [Government House] right now but we are peaceful people and won’t do that just yet,” he said.
Demonstrators say elections earlier this month, which were won by PM Valdimir Putin’s party, were rigged.
The government denies the accusation.
A sea of demonstrators stretched along Sakharov Avenue, a few miles from the Kremlin, in sub-zero temperatures.
Rallies are taking place across Russia, with the first big protest in the far eastern city of Vladivostok.
At least 28,000 people turned out in the capital, according to the Russian interior ministry, but rally organisers said the true number was around 120,000.
President Dmitry Medvedev announced political reforms this week, but many demonstrators say it is not enough.
They are demanding a re-run of the poll, which was won by Vladimir Putin’s party – but with a much smaller share of the overall vote.
As people braved the freezing temperatures, the Moscow mayor’s office was reportedly laying on tea and simple hot food from field kitchens.
Security is tight in the city, with 40 busloads of riot police lined up along the avenue, according to Russian media.
At one point, police manning metal detectors briefly closed access to the avenue, Interfax news agency reports.
‘We’re the power’
In Moscow, protesters clutched white balloons and banners with the slogan “For Free Elections” as the rally began.
This is a huge, mass movement of Muscovites, the BBC’s Daniel Sandford reports from the scene.
Mr Navalny, a prominent anti-corruption blogger who was jailed for 15 days over a street protest just after the elections, condemned Russia’s leaders as “swindlers and thieves”.
He listed victims of injustice including imprisoned former tycoon Mikhail Khodorkovsky and anti-corruption lawyer Sergei Magnitsky, who died in custody.
“Who’s the power here?” he shouted to cries of “We are” from the crowd.
“We are peaceful people but we can’t put with this forever.”
He promised that the next protest rally would be a “million strong”.
An eclectic line-up of 22 speakers were expected at the Moscow rally, with rival opposition figures addressing a crowd which mixed liberals with nationalists.
Alexei Kudrin, who recently resigned after serving a decade as Mr Putin’s finance minister, was booed when he took the microphone to condemn ballot-rigging and call for early parliamentary elections.
He warned that Russia faced the prospect of revolution if a dialogue was not established between the opposition and the authorities.
Some 50,000 people rallied on 10 December, in what was then biggest anti-government protest since the fall of the Soviet Union in 1991.
The opposition has been encouraged by that success, forcing the Kremlin on the backfoot.
On Thursday, Mr Medvedev proposed to hold direct elections of regional governors and simplify the procedure for registering political parties, but protesters say the concessions do not go far enough, the BBC’s Steve Rosenberg in Moscow says.
However, one of the main problems for the opposition is that there is no single leader able to unite it, our correspondent adds.
According to the official results of the elections to Russia’s Duma, the ruling United Russia party saw its share of the vote fall from 64% to 49%, though it remains easily the biggest party.
But there is a widespread view, fuelled by mobile phone videos and accounts on internet social networking sites, that there was wholesale election fraud and that Mr Putin’s party cheated its way to victory.
The Kremlin denies the claim.
In the Pacific port of Vladivostok, demonstrators carried posters calling for Mr Putin to be put on trial and regional MP Artyom Samsonov said the election results should be cancelled
Rallies against ballot-rigging were reported across Russia’s time zones on Saturday by Interfax
* In the Siberian city of Novosibirsk, a rally of between 800 and 1,500 people passed off peacefully
* About 100 people braved a frost of -15C in Orenburg on the border with Kazakhstan
* About 500 people rallied in Chelyabinsk in the southern Urals under the slogan “These elections were a farce! We want honest elections”
* Several arrests were made at a rally in St Petersburg, Vladimir Putin’s home city
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