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Another protester, 20-year-old statistics student Anatoly Ivanyukov, said attempts by authorities to disrupt the rally would only fuel more protest. “It’s like when you forbid children to do something, it makes them even more willing to do that,” he said.

The police investigators’ action follows the quick passage last week of a new bill that raises fines 150-fold on those who take part in unauthorized protests — fines that are nearly the average annual salary in Russia.

“I can’t predict whether I’ll leave here freely or in handcuffs,” Mr. Yashin told reporters before entering the Investigative Committee headquarters for the interrogation. “The government is doing everything possible so that I don’t end up there (at the protest).”

The top Twitter hashtag in Russia on Monday was “Welcome to the Year ‘37,” a reference to the height of the purges under Soviet dictator Josef Stalin.

Tuesday’s protest had city approval, but any shift from the location and time could give police a pretext for a crackdown.

Mr. Udaltsov urged protesters to march across town after the rally to the Investigative Committee’s headquarters to demand the release of political prisoners — an action that likely would trigger a harsh police response.

Many in the crowd, however, seemed reluctant to risk defying the authorities. Alexei Moiseyev, a student, said he wouldn’t risk attending Tuesday’s rally if it was unsanctioned.

“I’m not ready to enter into conflict with the law, even if these laws are questionable,” he said.

Mr. Nemtsov, speaking after Mr. Udaltsov, urged the demonstrators to act within the law.

“We must act in a responsible way, peacefully and calmly,” he said.

Sergei Parkhomenko, a leading journalist who helped organize Tuesday’s protest, said the authorities would like to see unrest to back their criticism of the opposition.

“They would be happy to stage some kind of provocation to prove that the people are just a herd of animals and the animals are always out of control,” he said.

A big opposition rally a day before Mr.  Putin’s inauguration in May ended in fierce clashes between police and protesters, and some opposition activists said the violence was provoked by pro-Kremlin thugs. The raids of the opposition leaders’ homes and their questioning were connected to that May 6 protest.

Andrey Bulay in Moscow contributed to this report.