MOSCOW—Tens of thousands of Russians on Saturday flooded a broad boulevard in the Russian capital, calling for an end to political controls under President Vladimir Putin and decrying police violence in previous weeks.

The biggest protest movement in Moscow in years has gripped the capital in recent weeks as loyalty to Mr. Putin has been waning among Russians who have seen their living standards slip under the weight of chronic economic problems and Western sanctions.

Protest organizers and an independent monitoring group said approximately 50,000 people had joined the authorized march that took place behind police cordons with hundreds of armored riot police looking on. Police said 20,000 had attended the rally.

Demonstrations have been held weekly since July against city authorities’ decision to ban some independent opposition politicians from running in coming Moscow city council elections due to alleged violations committed while collecting signatures to put forth their candidacy.

But numbers swelled on Saturday after some of Russia’s most famous internet celebrities and musicians promised to attend the demonstrations and called on their millions of social-media followers to do the same.