In the first reaction by a senior Russian official following Sunday's landslide victory for Zelensky, a comedian with no political experience, Medvedev said "there is a chance for improving cooperation with our country".
The result of the election, in which Zelensky roundly defeated incumbent Petro Poroshenko, "shows a clear demand for a new approach to solving Ukraine's problems", Medvedev wrote on his Facebook page.
Ukraine and Russia have been at odds since a 2014 uprising ousted a pro-Kremlin leader. Russia that year annexed Crimea and has backed separatists in a conflict in eastern Ukraine that has killed some 13,000 people.
Medvedev said he has "no illusions" about Zelensky.
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