"The [Russian] president congratulated Barack Obama on his inauguration and wished him every success," the report said. "The sides confirmed their readiness to make every effort to restore the potential of Russian-U.S. relations."
Obama was sworn in as the 44th president of the United States on Tuesday in Washington, becoming the country's first African-American head of state.
The Russian business daily Kommersant earlier said, citing a source close to the U.S. State Department, that Obama could pay a visit to Moscow in April.
According to the source, Obama will set off for his first European tour in April and is to visit London on April 2 to participate in the G20 summit, where he will meet with Medvedev for the first time.
Obama will then attend a NATO summit on April 3-4 in Strasbourg, France and Kehl, Germany to mark the 60th anniversary of the military alliance.
The source told Kommersant that Obama could fly to Moscow after the summit. The previous U.S. president, George Bush, flew to Russia's Black Sea resort of Sochi after last year's NATO summit in Bucharest.