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Russian election observers noted numerous reports of so-called “carousel voting,” in which busloads of voters are driven to different voting sites to cast multiple ballots.

Protest leaders have called for another rally in downtown Moscow on Saturday.

“Our votes were stolen,” said Dmitry Grishin, a student. “And we have to keep coming out on the streets.”

Attendance at Monday’s rally was markedly down from weekend protests in December and February, when crowds estimated at 100,000 demonstrated against parliamentary elections also criticized as fraudulent.

About 100 people were arrested at another rally in Moscow on Monday, when activists of the radical opposition group the Other Russia demonstrated near the office of the electoral committee.

Russia’s election chief, Vladimir Churov, is a loyal Kremlin figure who once said, “My first rule is that Putin is always right.”

About 300 people were arrested at an anti-Putin rally in St. Petersburg, Russia’s second-largest city.

In Washington, the State Department issued a muted response, pledging to work with the “president-elect” as soon as the election results are certified. However, the department did not mention Mr. Putin by name or offer congratulations to him.

The department urged Moscow to “conduct an independent, credible investigation of all reported electoral violations,” and said the United States was encouraged by the level of participation in the election.

“The number of Russian election observers who monitored this vote is unprecedented and a sign that Russian society seeks to participate in the improvement of Russia’s democratic institutions,” the statement read.

Sen. John McCain, a critic of the Russian leader, mocked Mr. Putin in a Twitter message, in which he referred to videos Sunday night of the Russian leader with tears in his eyes as he addressed supporters.

“Dear Vlad, Surprise! Surprise! You won,” the Arizona Republican said. “The Russian people are crying, too.”

c Guy Taylor contributed to this article, which is based in part on wire service reports.