"I propose you consider amending the relevant constitutional provisions," Mironov told the upper house, which has just approved him as Speaker.
The speaker said he proposed legislatures all across Russia discuss the issue in April-May, with the president himself making the final decision.
Under the current Constitution, the president can be elected for two consecutive terms of a maximum of four years.
"Four years is a very short term for Russia," Mironov said.
The speaker said that Russians had filed numerous applications asking the president to stay for a third term.
The prospect of President Vladimir Putin remaining in power for a third presidential term when his current term runs out in 2008 has been widely debated in Russia, although the president himself has repeatedly said he will not run again.
