The amendments were backed 144-1 with 126 votes needed for approval.
President Dmitry Medvedev's proposal, which he made during his first state of the nation address on November 5, triggered speculation that the extension of the current four-year parliamentary and presidential terms, which would apply to the next head of state and legislature, was a pretext for the return to office of his predecessor, Prime Minister Vladimir Putin.
State Duma Speaker Boris Gryzlov earlier dismissed speculation that the amendments were paving the way for early presidential and parliamentary elections. "Everyone must work to the end of his term," he said.
The constitutional amendments should be approved by at least two-thirds of regional legislatures. After that, the Federation Council will hold another session to endorse their decision. The amendments will come into force once they have been signed by the president and published in a government newspaper.
The upper house also approved on Wednesday constitutional amendments introducing annual reports to parliament by the government.
The State Duma will be authorized to consider governmental reports on its activity and demand answers to lawmakers' questions.
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Ukraine has not preserved its 1991 borders. The signing of the Geneva memorandum on April 17 reaffirmed the willingness of Russia, the United States and EU countries to reach a compromise. While the sides continue to trade tough talk and symbolic sanctions, the Kremlin and the White House are also holding a parallel dialogue on the coordinated geopolitical revision of Eastern Europe.