Putin, who secured almost 64 percent of votes on Sunday, portrayed his return for a third term as president as a victory over opponents who he said were trying to usurp power by undermining the Russian state.
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," anti-corruption blogger Alexei Navalny, one of the most influential opposition figures, told the crowd. "We are the power," he said to cheers, before being detained and taken away by the authorities.
Riot police in helmets then moved in to disperse several thousand protesters who stayed on the square, shoving away journalists and telling people to move on. Some were arrested at the rally which police said was attended by 14,000 people.
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 100 people were detained by riot police - about 50 at unsanctioned protests in Russia's northern city of St Petersburg and another 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 was slanted to favour 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."
The U.S. State Department called for an "independent, credible" investigation into all reported violations.
Although the monitors said there had been some improvements from a parliamentary poll which observers said was marred by irregularities on Dec. 4, they said Putin still had an advantage over his rivals in the media and that state resources were used to help him extend his domination of Russia for six more years.
Although the observers' findings have no legal bearing, they undermine Russian election officials' statements that there were no serious violations.
They would also support some in their view that elections ultimately have little real significance in Russia; that power is something tightly controlled and divided up by a largely stable ruling clique, as demonstrated by the 'tandem' power deal struck by Putin and current President Dmitry Medvedev in 2008.
Putin's opponents, fearing he will smother political and economic reforms, have refused to recognise the result, which could allow the former KGB spy to rule Russia for as long as Soviet leader Leonid Brezhnev, accused of presiding over "the years of stagnation".
"I used to love Putin, like any woman who likes a charismatic man. But now I think he is getting senile. Nobody can stay in power forever," Vasilisa Maslova, 35, who works in the fashion trade, said during the opposition rally.
"Voting yesterday, I felt like I was choosing the least dirty toilet in a crowded train station."
In a conciliatory move, Putin invited his defeated presidential rivals to talks, although Communist Party candidate Gennady Zyuganov did not attend.
The Kremlin also took steps that appeared intended to try to take the sting out of the protests which began over the Dec. 4 poll won by Putin's United Russia party.
Medvedev, who will stay in office until early May, told the prosecutor general to study the legality of 32 criminal cases including the jailing of former oil tycoon Mikhail Khodorkovsky.
Khodorkovsky, who headed what was Russia's biggest oil company, Yukos, and was once the country's richest man, was arrested in 2003 and jailed on tax evasion and fraud charges after showing political ambitions and falling out with Putin.
The Kremlin said Medvedev had also told the justice minister to explain why Russia had refused to register a liberal opposition group, PARNAS, which has been barred from elections.
The order followed a meeting last month at which opposition leaders handed Medvedev a list of people they regard as political prisoners and called for political reforms.
Medvedev's initiatives "have only one goal: To at least somehow lower the scale of dismay and protest that continues to surge in society," Zyuganov said.
