MOSCOW — Thousands of demonstrators turned out in Russia on Saturday as part of nationwide protests two days before Vladimir V. Putin’s inauguration for a fourth term as president.

In Moscow, the police clashed with protesters, turning a central square into a swirl of swinging nightsticks and shoving matches.

Protesters chanted, “Down with the czar!” And some wore paper crowns as a taunt against Mr. Putin’s lengthy rule, now extending longer than any Russian leader since Stalin.

A group that monitors arrests, OVD-Info, reported that by Saturday evening, the police had arrested 703 people in Moscow and about 1,600 throughout Russia. Among those arrested on Saturday was the opposition leader Aleksei A. Navalny, who had organized the rally, Russian news agencies reported.