The State Duma's constitutional legislation and state building committee chairman, Vladimir Pligin, said: "We will propose considering it in three readings in one session." The bill would then go to an immediate vote.
He said earlier on Wednesday that parliament may consider the amendments, submitted by President Dmitry Medvedev, on Friday. The move to consider the amendments in one session would vastly speed up the likely approval of the bill.
Medvedev has proposed increasing the presidential term to six years from four, and the term for the State Duma to five years from four.
Larisa Brycheva, a presidential aide, earlier said constitutional amendments to extend the term of office of the Russian president would not require a national referendum. Russian opposition groups have condemned the move.
The Russian Vedomosti paper said on Thursday, citing an unidentified Kremlin official, that Medvedev could resign next year, paving the way for the return of his predecessor and current Prime Minister Vladimir Putin.
The source told the paper that Medvedev may resign citing changes to the constitution, leading to presidential elections being held next year. Vedomosti said Putin could then rule for two six-year terms, from 2009 to 2021.
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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.