More than 3,300 protesters were arrested at demonstrations in support of jailed Kremlin critic Alexei Navalny, a monitor reported Sunday, as prosecutors probed possible violence "on the part of law enforcement".

Police clashed with demonstrators in Moscow as tens of thousands took to the streets across the country on Saturday following Navalny's call to protest against President Vladimir Putin's rule.

Putin's most charismatic critic was detained at a Moscow airport on arrival a week ago from Germany, where he had been recovering from a near-fatal poisoning with a nerve agent.

OVD Info, which monitors opposition rallies, said on Sunday that police seized at least 3,324 demonstrators across dozens of cities, with 1,320 people detained in Moscow and 490 in the second city Saint Petersburg.

It was the largest number of detentions at opposition rallies in the history of modern Russia. 

A number of protesters were injured at the rallies in the capital and Saint Petersburg.

Prosecutors in St Petersburg said in a statement late Saturday that they were probing violations including "on the part of law enforcement" and the use of force against an unidentified woman.

The statement was released after local media published a video showing a middle-aged woman falling to the ground after being kicked by riot police.

In the video, a woman - identified as Margarita Yudina - is seen asking three policemen in full riot gear why they were detaining a young unarmed protester. One of the policeman than kicks her in the stomach.

A representative of Saint Petersburg's Dzhanelidze hospital said that Yudina was hospitalised Saturday night with a head injury.

"She is in a serious condition," the hospital representative told AFP on Sunday. "She's in intensive care."

Saturday's protests took on an unprecedented geographic scale, spanning more than 100 cities across the country. 

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