Medvedev, 42, was inaugurated as Russia's third president since the collapse of the Soviet Union in 1991 last Wednesday, taking over from Vladimir Putin, who was approved as the country's premier by parliament on May 8.
While 48% of respondents in the poll said there would be no change in foreign policy, some 26% believe that relations between Russia and other states will improve, while only 5% expect relations to worsen. A total of 18% declined to answer.
Almost 50% of the respondents believe that no changes in the current foreign policy are needed. Some 36% of Russians believe that there is an urgent need for such changes.
In the poll, conducted in early April, around 30% of the respondents called ties with former Soviet states, such as Belarus, Ukraine and Georgia, a top priority in Russia's foreign policy. An overwhelming number of wealthy Russians said the country's main priority was relations with Europe.
Every fifth respondent said that Russia's foreign policy towards the West should be tougher, while only 6% of Russians said the president should be more 'pro-Western.'
Less that 10% of the respondents said a strengthening of ties with the U.S. should be a priority for the Russian president, who has been called a "straightforward fellow" by George Bush.
Bush and Medvedev met last month in Russia's Black Sea resort of Sochi. They are expected to renew their acquaintance in July at a meeting of the Group of Eight industrialized nations in Japan.
Medvedev, Putin's longtime ally, won a landslide victory in Russia's March 2 presidential elections, gaining more than 70% of the vote.
Putin's second term saw a rise in tensions with the West, as a resurgent Russia, awash with oil dollars, looked to reestablish itself as a global power. Moscow has strongly stated its opposition to NATO expansion and U.S. plans for a missile defense shield in central Europe.
However, unlike Putin, Medvedev has no links to Russia's 'siloviki,' representatives of the country's security and defense agencies.
Despite this, Putin has already said that the West will find Medvedev, seen as a pro-business moderate, no 'easier' to deal with.
"He is no less, in the best sense of the word, a Russian nationalist than I am. I don't think that our partners will find things easier with him," Putin said, adding that, "He is a real patriot, and will actively uphold Russia's interests on the global stage."
Medvedev's first official foreign visits as president will be to Kazakhstan and China in late May. The president is also set to visit Germany in early June.
The survey was carried out on April 5-6, and involved 1,600 respondents from 153 Russian regions. The error margin was 3.4%.