The Russian parliament has voted overwhelmingly in favour of a bill that would extend the next president's term of office from four to six years.
Two more readings of the bill are needed before it can become law.
President Dimitry Medvedev unexpectedly announced last week that he wanted to amend the constitution to enshrine the change.
Many observers say the move may signal that Prime Minister Vladimir Putin is planning a return to the presidency.
Meanwhile, Mr Medvedev has been warned by French President Nicolas Sarkozy about deploying missiles in the western enclave of Kaliningrad.
At a summit in the French resort of Nice, both sides agreed there should be no provocative moves before another meeting next year to discuss Mr Medvedev's security plans.
Mr Sarkozy also called on Moscow to complete its troop withdrawal from Georgia.