Putin was elected last year to a third non-consecutive term as president. His re-election was marred by protests and his administration has since cracked down on political opponents.
Less than 25 percent of the Russian citizens taking part in a survey conducted by independent polling company Levada Center told pollsters they wanted Putin to run for a fourth term in 2018, state-owned news agency RIA Novosti reported.
Putin boasts an approval rating of 64 percent among likely voters taking part in a similar survey by Levada in February. Of those taking part in the most recent survey, 8 percent said they wanted Prime Minister Dmitry Medvedev to run for president in 2018. Medvedev served as president while Putin was prime minister from 2008 to 2012.
Former Soviet leader Mikhail Gorbachev, who led the Soviet Union from 1988 until it dissolved in 1991, told the BBC early this year that Putin's policies were indicative of a leader concerned about his hold on power.
Levada interviewed 1,601 potential voters in 130 cities March 22-25. The survey had a margin of error of 3.4 percentage points.