Some 3,000 people have been arrested for taking part and prominent members of the opposition, including top Kremlin critic Alexei Navalny, remain behind bars.

Though a heavy police presence was seen in central Moscow earlier in the day, police steered clear of the activists.

At previous events police have used batons against protesters and grabbed people from the streets indiscriminately.

Earlier, around 4,000 people took part in an approved Communist Party rally for free elections, according to independent monitors.

The Communists are tolerated by the Kremlin and its veteran leader Gennady Zyuganov has said the party will not support the liberal opposition’s protest.

Many protesters came to the Communist rally with red Soviet flags. Many were middle-aged, some years older than those in the opposition rallies.

Prosecutors have launched criminal cases against about a dozen protesters for “mass unrest”, with potential prison sentences of up to eight years.

Putin’s 20 years on the global stage

They stand accused of offences, including throwing plastic water bottles at officers.

The Moscow city hall elections set for September 8 were, until last month, a relatively minor event on Russia’s political calendar.

But the issue blew up after election authorities refused to register various opposition candidates over alleged violations including faking the signatures needed to qualify.

Local polls are a rare opportunity for dissenting voices to participate in political life as anti-Kremlin parties have been squeezed out of parliament over Putin’s two decades in power.

The Kremlin commented on the month-long protests for the first time this week, seeking to play down the significance of the rallies.

“We do not agree with those who call what is happening a political crisis,” said Putin’s spokesman Dmitry Peskov, who defended an “absolutely justified” police response.

Video of a policeman punching a woman in the stomach as she was being detained after a sanctioned protest last week went viral. The interior ministry said it was opening an investigation.

Russian political scientist Ekaterina Shulmann said the cases against participants were “making people angry – they are broadly perceived as unjust and disproportionately cruel”.

While they have a “terrorising effect in the sense that people may be afraid to get out on the streets, at the same time they strengthen the protest mood because they are so blatantly unfair,” she said.

Independent analyst Masha Lipman said the protests were now more “emotional” than political.

“The protest movement is politically weak, there’s no clear goal,” she said, adding that many were “outraged” by the repressive actions of authorities.

Popular figures such as rapper Oxxxymiron and YouTube star Yury Dud have come out in support of the demonstrations, urging their fans and followers to go to sanctioned rallies.

Moscow has accused foreign governments and media of backing the protests, and next week Russian lawmakers will hold a special session to discuss the alleged “meddling”.

Meanwhile, authorities have upped the pressure on the opposition, focusing on Navalny’s anti-corruption foundation, which publishes investigations of officials close to Putin.

Investigators have raided the foundation’s office as part of a probe into alleged money laundering and a court froze the organisation’s accounts.