Image copyright AFP Image caption President Putin has dominated Russian politics for 20 years
Russian President Vladimir Putin has not ruled out running for president again beyond 2024, when his term ends.
But he told parliament that the Constitutional Court would first have to approve such a step. An MP has proposed "resetting to zero" the number of presidential terms.
Mr Putin, 67, could potentially stay in power until 2036, by winning two more six-year terms.
The former Soviet KGB officer has been in power for 20 years.
Mr Putin however rejected as "not expedient" a different proposal that would simply lift the current prohibition on a president serving more than two consecutive terms.
By serving as prime minister in 2008-2012, Mr Putin remained at the pinnacle of power without violating the two-term rule. His close ally Dmitry Medvedev was president for those four years.
The amendments addressed by Mr Putin in his televised speech on Tuesday were put forward by MP Valentina Tereshkova, the first woman in space and a strong supporter of his presidency. Most MPs in parliament - the State Duma - are pro-Putin.
Russia will hold a "public vote" on 22 April to decide if constitutional changes will go ahead. They could significantly alter the balance of power between the presidency and parliament.
Media playback is unsupported on your device
Media captionOrdinary Russians have taken to appealing directly to Putin to solve their problems
The "reset to zero" proposal would, according to Mr Putin, mean "removing the restriction for any person, any citizen, including the current president, and allowing them to take part in elections in the future, naturally in open and competitive elections".
It could go ahead if approved by citizens in the public vote on 22 April, he said, and "if the Constitutional Court rules such an amendment would not go against (the constitution)".
That amendment has now been approved by the Duma.
Image copyright Reuters Image caption In 1963 Valentina Tereshkova, as a Soviet cosmonaut, became the first woman in space
Mr Putin also said he saw no need for early elections to the Duma, rejecting another MP's proposal.
He triggered intense debate about changing the constitution when, unexpectedly, he put forward draft amendments in January. He proposed transferring some powers from the presidency to parliament.
In his speech on Tuesday, he said "a strong presidency is absolutely essential", but he added that the Duma "should get wider powers".
Such changes were needed, he said, "to strengthen our sovereignty, traditions and values" in a world in the throes of fundamental change, including new challenges such as digital technology and coronavirus.
In the long term, he said, Russia "needs a guarantee that the people in power can be changed regularly", and he insisted that "elections must be open and competitive".
He also ruled out a Western-style parliamentary system, remarking that "for years in some European countries they cannot form a government".