About 2,500 people gathered in Moscow alone, and police made more than 800 arrests nationwide.
The videos showed Mr Navalny calling for Russians to take part in protests on 9 September against raising the retirement age.
Even so, demonstrations took place in more than 80 towns and cities Sunday after opposition leader Alexey Navalny had urged Russians to protest the measures.
Navalny didn't take part in the protests, as he's now serving a 30-day sentence for violating public demonstration laws.
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Putin's trust rating in public opinion polls dropped notably after the proposal was put forward and last month offered some concessions, including dropping the age for women from 63 to 60.
Russia's ruling United Russia Party suffered a rare setback in regional elections on Sunday despite winning most of the seats, a reversal its leaders and election chiefs blamed on unpopular plans to raise the pension age.
The proposed pension changes, which are now going through parliament, have shaved around 15 percentage points off Putin's popularity rating and are the most unpopular government measure since a 2005 move to scrap Soviet-era benefits.
The demonstrators, predominantly people in their 20s and decades away from retirement, chanted "Russia without Putin" and held signs with messages such as "Putin, when will you go on pension?"
Riot police ordered the crowd to disperse or face prosecution. Sobyanin traditionally came to polling station number 90 on Nikolayeva Street.
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Navalny, who ran against Sobyanin in 2013 and had planned to lead a protest against proposed pension changes on Sunday, will spend election day behind bars after being convicted of violating protest laws.
Protests have begun in Vladivostok and other cities in Russia's Far East.
Elections to select the heads of 26 of Russia's 85 regions are also being held on Sunday, including in Moscow. In Yakutsk's mayoral contest, Sardana Avksentyeva, of the Party for the Renaissance of Russia, beat Aleksandr Savinov, of the pro-Putin United Russia.
Data from the World Bank in 2016 shoes that 43 percent of Russian men are not expected to reach the age of 65, with the average life expectancy for men in Russia sitting at 66 for men and 77 for women.
Sergei Sobyanin, mayor of the Russian capital since 2010, won a predictable victory with 70.02 percent of the vote. The authorities refused to authorize most of the meetings, declaring them illegal.
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Four-year-old Mckenzie Brackley was at the event to pick up an award for his courageous battle with Acute Flaccid Paralysis. Meghan , Duchess of Sussex attends the WellChild awards at Royal Lancaster Hotel on September 4, 2018 in London , England.