White House Press Secretary Sean Spicer condemned the arrests and called on Russian Federation "to release all peaceful protesters". The protesters were shouting "Putin is a thief", "Putin out" and "Russia without thieves". In Moscow, thousands of angry protesters held an unsanctioned rally on Tverskaya, the capital's main street.
Navalny's wife, Yulia, said he had been detained as he tried to leave their home.
Russian Federation ranked 131st place out of 176 countries in the 2016 Corruption Perception Index of Transparency International.
Almost 200 rallies were planned for towns and cities to mark the Russia Day public holiday.
Medvedev dismissed Navalny's allegations as politically motivated "nonsense" and called the opposition politician a muck-raking charlatan.
Navalny, who had a green liquid thrown in his face in April, robbing him of some of his sight, said hundreds of people had also attended demonstrations in Russia's Far East on Monday morning. Spicer called on the Russian government to immediately release all peaceful protesters. Authorities had given permission for the rally, but Navalny late Sunday called for the location to change to one of Moscow's main avenues.
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"Change is always good", Sukhoruchenkov said, adding that he and his friends were concerned about corruption - Navalny's rallying cry - that "manifests itself in all areas: from traffic police to university professors".
Electricity in his office was cut at around the same time as he was detained, briefly bringing down a live feed of nationwide protests, Navalny's spokeswoman said.
An unlikely object of dispute emerged at the St. Petersburg demonstration: As Russian journalist Arseny Vesnin and others noted, a giant yellow duck was among those detained by police, after being batted around in the air by the crowd.
A regional security official, Vladimir Chernikov, told Ekho Moskvy radio that police would not interfere with demonstrators on the street - as long as they did not carry placards or shout slogans.
Policemen detain a supporter of opposition leader and anti-corruption blogger Alexei Navalny near a court building during his hearing in Moscow December 30, 2014.
The protests in March took place in scores of cities across the country, the largest show of discontent in years and a challenge to President Vladimir Putin's dominance of the country. Authorities have said the protest is illegal.
The center of the Moscow protest is at Pushkin Square - and while NPR's Mary Louise Kelly says the crowd there is huge, she adds that it's also hard to ascertain how many people are there for Navalny's cause, and how many for the national holiday. He said contractors hired to build a stage at the agreed-upon venue could not do their work after apparently coming under official pressure. Most recent was in March when he, and up to 1,000 others, were arrested during rallies which aimed to unseat Prime Minister Dmitry Medvedev over corruption concerns.
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