The protests against Putin, who many feel was re-elected through an unfair election process, were called by opposition leader Alexei Navalny, who was himself detained at a demonstration in the capital, Moscow.
Does Putin's Russian Federation reject the West? Iraida Nikolaeva screamed, operating after police in Moscow after they detained her son.
Saturday's rallies were smaller than the ones that preceded Putin's last inauguration, in 2012, when some 100,000 turned out in Moscow alone in a wave of winter and spring protests.
AFP reported that tear gas had been briefly used.
Navalny and his ally, Nikolai Lyaskin, were among about 500 detained in Moscow as police violently attempted to disperse an unsanctioned rally, the group said.
Putin is due to be sworn in for his fourth term as Russia's president on May 7. In the Urals city of Yekaterinburg, around 1,500 km east of Moscow, a Reuters reporter saw a crowd of more than 1,000 people protesting, some shouting "Down with the Tsar!"
Of them, more than 700 were detained in Moscow and more than 230 in second city Saint Petersburg.
A protester tries to brake through a police line during a demonstration against President Vladimir Putin in Pushkin Square in Moscow, Russia.
Video posted on Navalny's YouTube channel showed the wide Nevsky Prospekt avenue blocked off around Gostiny Dvor, the sprawling trade complex that is one of the city's landmarks. "Putin is not a tsar to be sitting (at the Kremlin) forever".
The protests demonstrated that Mr Navalny's opposition, although considered beleaguered by officials and largely ignored by state-controlled television, has sizeable support in much of the country.
Demonstrations below the slogan "He's not our czar" befell all through the nation, from Yakutsk within the far northeast to St. Petersburg and Kaliningrad on the fringes of Europe.
According to OVD-Info, a website which monitors arrests, 1,029 arrests were made in 19 cities across Russian Federation, almost half of them in Moscow.
"We don't have the hope that we'll make Russian Federation wonderful and prosperous overnight, " Leonid Volkov, Navalny's chief of staff, said on the Navalny team's live YouTube broadcast encouraging people to join the protests.
Navalny had called for demonstrations in more than 90 towns and cities across Russian Federation against what he says is Putin's autocratic, tsar-like rule.
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