At least 30 people were reported to have been held in St Petersburg and more than 16 in the southern city of Kemerovo.
Activists in some other cities were kept away from protests, reports said.
President Putin has not confirmed that he will run in March 2018 but he is widely expected to do so.
The rallies - held under the slogan "We're sick of him" - were organised by the Open Russia movement founded by former oil tycoon Mikhail Khodorkovsky.
Mr Khodorkovsky, a fierce critic of President Putin, lives in exile after spending 10 years in a Siberian prison on fraud charges, which he says were politically motivated.
Protesters also held an unauthorised rally in central Moscow on Saturday, but the presidential reception office, to which they planned to submit letters, was blocked off.
A journalist with AFP news agency in St Petersburg said about 200 people had gathered for the rally and at least 30 protesters were taken away by authorities.
Open Russia put the figure at about 50 people while OVD-Info, which monitors the detentions of political activists, said more than 125 had been detained. Police did not release official figures.
"Putin is an usurper. He has to finally go. We're sick of him," said one protester in St Petersburg, quoted by AFP.
"Everything is bad. Education, health - everything has been destroyed. I want changes," said another.
The protests come days after Russia opposition leader Alexei Navalny was taken to hospital when a green antiseptic solution was splashed in his face.
Mr Navalny is one of Russia's foremost critics of President Putin and has announced his intention to run for president himself.
However, a conviction for embezzlement - which he denies - would bar him from running for office.
Mr Putin has been a dominant political figure in Russia since his election as president in 2000.
He served two terms and then a four-year stint as prime minister, before resuming the presidency in 2012.
|Officers from the Russian interior ministry detained protesters in St Petersburg. Reuters|
Russian police arrest dozens of anti-Putin protesters
More than 100 activists were arrested in St Petersburg on Saturday as hundreds of Russians turned out to protest against President Vladimir Putin's expected candidacy in elections next year.
Demonstrators rallied across several cities under the slogan "We're sick of him."
The protests were called by the Open Russia movement founded by Kremlin critic Mikhail Khodorkovsky.
About 200 people gathered in central St Petersburg, according to AFP news agency. OVD-Info, which monitors political repression, said more than 110 protesters were hauled away by riot police.
"Police officers ended the actions ... of 100 people who continued to trouble the public order," St Petersburg police said, without confirming if they had been arrested.
Putin, 64, has not announced whether he plans to run for president again. He has dominated Russian politics for 17 years and enjoys high popularity ratings.
"Putin is an usurper. He has to finally go," said one of the protesters, 35-year-old Anton Danilov, in St Petersburg.
"Everything is bad. Education, health - everything has been destroyed. I want changes," said Galina Abramova, 57.
In Moscow, a similar sized rally remained peaceful as activists lined up under the gaze of riot police to hand over handwritten appeals for Putin to stand down from running in 2018.
"I don't want Putin to stand in the next elections," said Anna Bazarova, a 16-year-old student queuing up to hand in her petition. "Our main problem is that we can't change those in power."
Police said 250 people showed up in Moscow, the Interfax news agency reported, while Maria Baronova, an Open Russia activist, said at least 500 people had handed over a petition.
OVD-Info reported more arrests in other cities, including 20 in Tula and 14 in Kemerovo.
Saturday's protests came after opposition leader Alexei Navalny organised the largest unauthorised rally of recent years in Moscow on March 26. Police detained about 1,000 people, including Navalny.
Authorities have stepped up pressure on Khodorkovsky's Open Russia in recent days.
The General Prosecutor's Office ruled on Wednesday that the activity of its British arm was "undesirable" and accused it and other organisations of trying to discredit the election.
On Thursday, police searched Open Russia's Moscow offices. Activists said they confiscated 100,000 blank appeal forms that the foundation had intended to distribute to people encouraging them to call for Putin to quit.
Russian rallies urge Putin not to run again; dozens arrested
MOSCOW) — Under the slogan "I'm fed up," demonstrators urging Vladimir Putin not to run for a fourth term rallied in cities across Russia on Saturday. Dozens were arrested in St. Petersburg and elsewhere.
The centerpiece rally in Moscow went peacefully, despite being unsanctioned by authorities. Several hundred people rallied in a park then moved to the nearby presidential administration building to present letters telling Putin to stand down from running in 2018.
But in St. Petersburg, Associated Press journalists saw dozens arrested. The OVD-Info group that monitors political repression relayed reports of more arrests in several cities, including 20 in Tula and 14 in Kemerovo.
Putin has not announced whether he plans to run for president again next year.
He has dominated Russian politics since becoming president on New Year's Eve 1999 when Boris Yeltsin resigned. Even when he stepped away from the Kremlin to become prime minister in 2008-2012 because of term limits, he remained effectively Russia's leader.
Nationwide protests on March 26 appeared to rattle the Kremlin because of the demonstrations' unusual size and reach. The predominance of young people in those protests challenges the belief that the generation that grew up under Putin's heavy hand had become apolitical or disheartened.
Saturday's demonstrations were much smaller, but indicated that marginalized opposition forces will continue to push.
The demonstrations were called for by Open Russia, an organization started by Kremlin foe Mikhail Khodorkovsky.
As an oil tycoon, Khodorkovsky was once listed as Russia's richest man, but his political ambitions put him at odds with the Kremlin. He was arrested in 2003 and served 10 years in prison on tax-evasion and fraud convictions that supporters say were political persecution. He was pardoned in 2013, left the country and revived Open Russia as a British-based organization.
On Wednesday, Russia's Prosecutor-General banned Open Russia as an undesirable foreign organization. But the group's Moscow branch says it is administratively separate and not subject to the ban.