Putin, who secured almost 64 percent of the votes on Sunday, portrayed his return to the presidency as a triumph over opponents who were trying to usurp power, though international monitors said the vote was clearly skewed in his favour.
But opposition leaders said they drew 20,000 people into Moscow's Pushkin Square, the scene of dissident protests during Soviet times, to call for new elections and an opening up of the political system crafted by Putin during his 12-year rule.
"They robbed us," Navalny, an anti-corruption blogger, told the crowd before his detention. "We are the power," he said to chants of "Russia without Putin."
The atmosphere at the rally was jovial at first, but became tense when riot police in helmets moved in to disperse several thousand activists who stayed on the square.
Encircling one group of protest leaders huddled in a fountain closed down for winter, black-helmeted riot police detained Navalny, 35, and others, marching them to waiting police vans.
Opposition leaders said 500-1,000 people were arrested but police put the number at 250 and said 14,000 people had attended the rally.
Thousands of Putin supporters staged rallies closer to the red walls of the Kremlin, singing songs, waving Russian flags and chanting Prime Minister Putin's name.
At least a further 350 people were detained by riot police - about 300 at unsanctioned protests in the northern city of St Petersburg, Putin's home town, and 50 at Moscow's Lubyanka Square, the seat of the Soviet-era KGB. Up to 3,000 people turned out in St Petersburg, witnesses said.
Putin says he won a six-year term as Kremlin chief in a fair and open contest, but vote monitors from the Organization for Security and Co-operation in Europe echoed the opposition's complaints that the election had been slanted to help him.
"The point of elections is that the outcome should be uncertain. This was not the case in Russia," Tonino Picula, one of the vote monitors, said on Monday. "According to our assessment, these elections were unfair."