MOSCOW - President Putin of Russia said he would support legislation to let him run for two more terms. That could keep him in power until 2036.

Citing the need for stability, the Russian leader said he should be allowed to seek two more terms, if the Constitutional Court agrees.

The proposal, unexpectedly floated by a lawmaker at a session of Russia’s lower house of Parliament, would allow Mr. Putin — who is 67 years old and was first elected president in 2000 — to remain in power until at least 2036.

After lawmakers voiced support for the idea, Mr. Putin arrived in person at the State Duma to say he agreed with it, in what appeared to be a tightly choreographed course of events. Mr. Putin said he believed he should have the right to run again for the sake of Russia’s stability, even though future presidents should continue to be bound by a two-term limit.

It appeared that under the proposal endorsed by Mr. Putin, the limit of two six-year terms would be reset for him if he were to run again when his current term ends in 2024.

The president is the guarantor “of the security of our state, of its internal stability — its internal, evolutionary stability,” Mr. Putin said. “And I mean evolutionary. We’ve had enough revolutions.”

Currently, the Russian Constitution bars presidents from serving more than two consecutive terms. This would mean that Mr. Putin — who served as president from 2000 to 2008, as prime minister from 2008 to 2012, and again as president since 2012 — would need to step down when his current term ends in 2024.