Medvedev announced the idea in his state of the nation address on November 5.
"I back President Medvedev's proposals. Proposals connected with amendments to the Constitution have no personal dimension. Regarding who could run for the next term and when, it is too early to discuss this," Putin told journalists.
Putin said Medvedev's proposals were aimed at improving the system of government. Media have reported that the changes would be used as a pretext to return Putin to the presidency.
"We are looking for such instruments that would guarantee the implementation of our long-term plans and boost the development of democratic processes in the country, rather than do any harm," the premier said.
Explaining his opinion to a journalist from Finland, where the presidential term is six years, Putin said the president's initiative contained "nothing unusual."
The Vedomosti business daily 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 could 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.
A senior member of the ruling United Russia party quoted by the daily said the initiative to extend both the presidential and parliamentary terms was the beginning of constitutional reforms designed to turn Russia into a parliamentary republic.
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.