MOSCOW -- President Vladimir Putin's spokesman is taking issue with White House criticism of the arrests of hundreds of opposition protesters.

Anti-corruption demonstrations took place Monday in scores of cities throughout Russia. More than 850 people were reportedly arrested in Moscow and about 500 in St. Petersburg, where the rallies were unsanctioned.

CBS News correspondent Elizabeth Palmer reported that one of Putin's most prominent political rivals, Alexei Navalny, the organizer of the day of protests, was arrested as he left his Moscow apartment on the way to join one of the demonstrations.

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Tens of thousands of people still took to the streets, and more than 1,500 were arrested across the vast country.

White House press secretary Sean Spicer on Monday said the United States "strongly condemns the detention of hundreds of peaceful protesters" which he described as an "affront to core democratic values."

But Kremlin spokesman Dmitry Peskov said Tuesday that "We do not agree with such a statement of the question."

Peskov added: "For those who engaged in provocative actions in violation of the law, the actions of the authorities were taken in full compliance with our legislation."

Russia's government tried to head off the demonstration in Moscow by banning it from going ahead in the center of the city. But CBS News' Palmer watched as huge crowds of demonstrators ignored the ban and crashed the country's national Russia Day holiday celebration, chanting, "Putin is a thief."

There was a standoff at the front line of the protests. Demonstrators managed to get into an area that was specifically banned to them, then the riot police showed up and tried to stop anyone else from joining the mass of protesters.

Danil Beylakov, 15, was helping spread the word of the protests in the town of Vladimir, about 150 miles of Moscow.

"Russia is an authoritarian regime, and I want to change it into a Democracy," he told CBS News.

That, Palmer noted, is a tall order, but there's no question Navalny has touched a nerve inside the Kremlin.

One of the protesters summed up the sentiment as he was led away from the Moscow demonstration by the police, turning to cameras and shouting, "Russia, will be free!

Navalny -- who set it all in motion -- was whisked through his court hearing on Monday and handed a 30 day prison sentence.