Fifty-five percent of those surveyed by the Levada Center -- an independent, non-governmental polling and sociological research group -- said they wanted a new leader, while 22 percent said they wanted Putin re-elected to another term, RIA Novosti reported Thursday.
That's an improvement for Putin. A survey last year found 17 percent wanted him as president for another six-year term.
Only 8 percent said they wanted Prime Minister Dmitry Medvedev, who was president from 2008 to 2012, to be president again.
A Levada survey in February said Putin was still popular with 64 percent of those polled. That poll found Putin would be the most popular, at 32 percent, of a potential list of candidates if an election had been held then.
Only 36 percent of those voters who supported Putin last year want him to remain in office for a fourth term, said Alexei Grazhdankin, deputy head of the Levada Center.
Half of those surveyed said keeping Putin in power would help the country, while a third said another term for Putin would not be good for Russia.
The survey of 1,601 people in 130 communities in 45 Russian regions was conducted March 22-25. The margin of error was 3.4 percentage points.
Ukrainian protestors topple Lenin statue [VIDEO]
Reindeer recovered after escaping from Santa during lighting ceremony