MOSCOW — The Russian police detained more than 800 people protesting planned increases to the retirement age on Sunday, a rights group said, disrupting demonstrations against an unpopular change that has hurt President Vladimir V. Putin’s approval rating.

The protests, organized by the jailed opposition leader Alexei Navalny and his supporters, were a challenge to the authorities, who were hoping for a high turnout at regional elections being held on Sunday.

Footage of the protests, which were held in more than 80 towns and cities, showed the police sometimes using force to disperse rallies, beating participants with batons and dragging them away. The authorities declared most of the protests illegal.

OVD-Info, a rights organization that monitors detentions, said 839 people had been detained by the police in 33 cities, including some of Mr. Navalny’s closest aides.