Thousands of people have attended the biggest anti-government rally in the Russian capital Moscow since the fall of the Soviet Union.
As many as 50,000 people gathered on an island near the Kremlin to condemn alleged ballot-rigging in parliamentary elections and demand a re-run.
Other, smaller rallies took place in St Petersburg and other cities.
Communists, nationalists and Western-leaning liberals turned out together despite divisions between them.
The protesters allege there was widespread fraud in Sunday's polls though the ruling United Russia party did see its share of the vote fall sharply.
Demonstrations in the immediate aftermath of the election saw more than 1,000 arrests, mostly in Moscow, and several key protest leaders such as the anti-corruption campaigner Alexei Navalny were jailed.
Prime Minister Vladimir Putin has never experienced popular protests like these before, the BBC's Steve Rosenberg reports from Moscow.
During his decade in power, first as president then prime minister, he has grown used to being seen as Russia's most popular and powerful politician.
But as one of the protesters put it to our correspondent, Russia is changing.
'We are the people'
Police put the number gathering on Moscow's Bolotnaya Square for the "Fair Elections" rally at 25,000 while organisers talked of 100,000.
The BBC's Daniel Sandford reports from the scene that the number seems to be closer to 50,000, and people continued to rally on the square after hearing the speakers.
A resolution was passed calling for the cancellation of Sunday's election results, new elections, the resignation of electoral commission chief Vladimir Churov, an investigation into the alleged ballot-rigging and the immediate release of arrested protesters.
Authorities had permitted the protest on condition the rally was relocated from central Revolution Square to Bolotnaya Square, an island in the Moscow River just south of the Kremlin where access points could be easily controlled.
Marchers to the rally streamed across a bridge under the walls of the Kremlin walls, past a long line of police.
Prominent figures at the rally included younger opposition activists like Yevgenia Chirikova, as well as former Prime Minister Mikhail Kasyanov and Boris Nemtsov, a former deputy prime minister under the late Boris Yeltsin.
"Our action is peaceful, we hold the most civilised protest on planet," Ms Chirikova told reporters on her way to Bolotnaya.
Sergei Mitrokhin of the liberal Yabloko party told the crowd: "Putin and [President Dmitry] Medvedev made a shocking discovery today.
"Russia has people. We are the people."
At least 50,000 police and riot troops were deployed in Moscow ahead of Saturday's protests and the city began to resemble a police state rather than a democracy, Daniel Sandford says.
There were no immediate reports of protest-related arrests in Moscow but police in Kurgan, on the border with Kazakhstan, dispersed an unapproved rally.
Demonstrations were held from Vladivostok in the far east to Perm in the Urals, from Arkhangelsk in the Arctic north to Kaliningrad in the far west.
In St Petersburg, Russia's second city, thousands packed into Pionerskaya Square to hear speeches calling for the election to be re-run and for Mr Putin to resign, the BBC's Richard Galpin reports.
The protest was peaceful and well organised though some protesters were dragged away by police.
One student organiser who had never taken part in protests before said people could not tolerate what he said was the massive falsification of the parliamentary election.
Police put the turnout in the city at 10,000.
In Vladivostok, seven time zones to the east of Moscow, several hundred people marched.
Advice to Medvedev
According to the official results of the elections to Russia's Duma, United Russia 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.
On Friday, the presidential Council for Human Rights advising Mr Medvedev said the reports of vote-rigging were of deep concern, and that the elections should be rerun if they were confirmed.
However the council has no power to order a fresh ballot, correspondents say.
Mr Putin, who was president between 2000 and 2008, remains widely predicted to win a presidential election in March.
On Thursday, he blamed the US for stoking the recent unrest, after Secretary of State Hilary Clinton expressed reservations over the poll.
The prime minister said Mrs Clinton's remarks had "set the tone for some opposition activists".