Russian opposition leader Alexei Navalny and dozens of others have been arrested as thousands of people across Russia defied bans on rallies to protest against government corruption.

The demonstrations on Sunday were organised by Navalny, a Kremlin critic and anti-corruption campaigner, who urged people to take to the streets to demand the resignation of Prime Minister Dmitry Medvedev.

"Don't try to fight for me," Navalny wrote on Twitter after police in Moscow put him in a minibus, urging people to stay with the rally. "Our issue today is the fight against corruption."

Navalny called for the protests after publishing a detailed report this month accusing Medvedev of controlling a property empire through a shadowy network of non-profit organisations.

Medvedev, who has so far made no comments on the claims, is accused of amassing a private collection of mansions, yachts and vineyards. As the alleged luxuries include a house for raising ducks, many of the placards in the protests showed mocking images of yellow toy ducks.

The protests, which attracted crowds of hundreds or thousands in most sizeable Russian cities, were the largest coordinated outpourings of dissatisfaction in Russia since mass protests in 2011-2012.

Navalny's website had previously said that more than 80 towns and cities across Russia would hold protests on Sunday and that authorities had not sanctioned the majority of the rallies.

Al Jazeera's Rory Challands, reporting from Moscow, said the "big story" of the day was the number of demonstrations taking place across Russia.

"That is rare," he said. "This suggest that Alexei Navalny's anti-corruption message is really resonating at the moment in Russia, in a way that more generalised anti-government messages don't.

"When people feel like the politicians above them are cheating them, that it seems is when Russians get angry and stand up and do something."

Russian authorities had warned Navalny's supporters on Friday not to attend the rally because the event had not been sanctioned by the city administration.

The Russian constitution allows public gatherings but recent laws have criminalised protests not authorised by city authorities, who frequently refuse to grant permission for rallies by Kremlin critics.

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In the far eastern city of Vladivostok, a Reuters news agency reporter saw the arrest of at least 30 protesters at an unsanctioned rally drawing hundreds of young people to a square near the city's railway station.

The arrests started after protesters unfurled banners reading "Corruption steals our future" and "The prime minister should answer".

The protesters then marched to a police station to demand that those arrested be freed.

Hundreds also rallied in the city of Yekaterinburg in the industrial Urals region.

Witnesses said at least four people holding banners were arrested on the city's Labour Square, where opposition protesters, nationalists and supporters of the pro-Kremlin United Russia party gathered.

Police said 500 to 700 people had gathered on Labour Square but did not confirm that there had been any detentions.

"Corruption affects every person. The fight against corruption can unite all people irrespective of their convictions," 20-year-old student Ivan told Reuters, asking that his last name not be published.

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Some demonstrators have protested with their faces painted green, a reference to a recent attack on Navalny when an assailant threw a green anti-septic liquid in his face.

In February, a Russian court found Navalny guilty in a retrial of a 2013 fraud case, which barred him from running for president next year.

Judge Alexei Vtyurin handed down a five-year suspended prison sentence and a fine of about $8,500 to Navalny for embezzling timber worth about $500,000.

Navalny, 40, pledged to appeal against the "politically motivated" ruling and continue with his plans of challenging President Vladimir Putin in the forthcoming presidential elections, even though the Russian law bars anyone convicted of a crime from running for a public office for 10 years.