When asked "Who holds the real power in the country?" more than a third - 36% - said Prime Minister Vladimir Putin did, while only 9% saw Medvedev as the main figure.
Almost half - 47% - answered that power was shared by "both equally." Eight percent gave no answer.
Medvedev, 42, was inaugurated as Russia's third president since the collapse of the Soviet Union in 1991 on May 7, taking over from Putin, who was approved as the country's premier a day later.
When pollsters asked the same question in March, after Medvedev had been elected president but before Putin had stepped down, the public's view was that power was shared more equally.
Those who said power was divided equally constituted 47%, while 21% picked Putin as the real leader and 20% went for Medvedev. Twelve percent were unable to answer.
The current poll also indicated that 51% of Russians believe Medvedev in general continues his predecessor's policies. Thirty-one percent were sure Medvedev's policies are the same - up 5 percentage points from March.
Eleven percent said Medvedev is gradually altering his policies, while only 2% said the new president governs the country in his own way.
The poll was conducted July 18-22, 2008. A total of 1,600 Russians were polled in 128 cities and villages in 46 regions. The margin of error was 3 percentage points.
