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Recent changes to the constitution, pushed through the parliament by United Russia, would allow Mr. Putin to serve as president until 2024 if he is re-elected.

“When I heard that these guys are supposed to govern our country for 12 more years, I realized I wouldn’t know what I could say to my small daughter when she eventually asks me, ‘Why didn’t you do something?’” protester Ilya Fainberg said.

Russia’s opposition has called for new protests Dec. 24 if the Kremlin does not agree to new parliamentary elections.

But it’s unclear whether the opposition will be able to sustain the protests throughout the long, cold winter to come.

Still, for many in the crowd Saturday, the protest was simply confirmation that there are others willing to make public their opposition to Mr. Putin.

“This rally isn’t about what we are saying to the authorities,” Moscow student Ruslan Dudenkov said. “They don’t give a damn about us — yet. The most important things is what it says to other people, other protesters. We are telling them, ‘You are not alone.’ “