At least 31 people have been arrested during opposition protests in Moscow, the second Sunday in succession to see such demonstrations.
Last week, at least 1,000 people were held during protests in Moscow, reportedly the largest in five years.
The opposition has called for the resignation of Prime Minister Dmitry Medvedev over corruption allegations.
A smaller group of about 100 people began marching through Moscow on Sunday, but were blocked by police.
While police said 31 people had been detained for "breaches of public order", OVD-Info, a website monitoring detentions, said 56 people including four minors were arrested.
Those who organised the protest via social media are now facing an investigation.
Last Sunday's demonstrations in Moscow and across the country were prompted by main opposition leader Alexei Navalny, who was later arrested.
Police said 500 people were held, but OVD-Info said at least 1,000 people were arrested in Moscow alone.
Mr Navalny had published reports claiming that Mr Medvedev controlled mansions, yachts and vineyards - a fortune that far outstripped his official salary.
The prime minister's spokeswoman called the allegations "propagandistic attacks", but the prime minister himself has not commented on the claims.
Alexei Navalny has announced his intention to run for president in 2018 against Vladimir Putin. But he is barred from doing so after being found guilty in a case he said was politicised.
Mr Navalny was sentenced to 15 days in prison for his role in last Sunday's demonstrations. His spokesman said on Twitter that he had nothing to do with the new protest.
Organisers told news agencies that they had planned to march towards the Kremlin on Sunday when they were stopped by police.
Witnesses said police had detained people photographed at the previous rally. "You could see they were acting in a targeted way," protester Natalya Ponomarenko told AFP news agency.
Russia's Interfax news agency reported that about 400 people had taken part in an authorised anti-corruption rally in the Siberian city of Novosibirsk.