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In an apparent bid to assuage the opposition anger, outgoing President Dmitry Medvedev told the Justice Ministry to present its explanation for last year’s rejection of registration for the People’s Freedom Party, an organization led by some of the opposition’s most prominent figures.

He also ordered the prosecutor-general to re-examine the legality of the conviction of imprisoned former oil tycoon Mikhail Khodorkovsky and more than 30 others regarded by the opposition as political prisoners.

Political analysts and opposition activists saw the move as an attempt to soothe protesters, but they said it remains to be seen if it results in any action.

The West can expect Mr. Putin to continue the tough policies he has pursued even as prime minister, including opposing U.S. plans to build a missile shield in Europe and resisting international military intervention in Syria.

The U.S. administration congratulated the Russian people for turning out to vote in big numbers in Sunday’s election, but it also expressed concern about allegations of fraud and urged a full investigation into the charges.

The State Department said Monday that the U.S. would work with Russia’s “president-elect” once the votes are certified, but it pointedly did not mention Mr. Putin by name or offer any congratulations to him.

Communist Party candidate Gennady Zyuganov was a distant second in the election, followed by Mikhail Prokhorov, the billionaire owner of the New Jersey Nets basketball team, whose candidacy was approved by the Kremlin in what was seen as an effort to channel some of the protest sentiment. Mr. Prokhorov attended Monday’s protest.

The clownish nationalist Vladimir Zhirinovsky and socialist Sergei Mironov trailed behind. The leader of the liberal opposition Yabloko party was barred from the race.

Associated Press writers Jim Heintz, Peter Leonard, Mansur Mirovalev and Vladimir Isachenkov in Moscow; Irina Titova in St. Petersburg; and Don Melvin in Brussels contributed to this report.