Today attacks on the Belgian capital's international airport and a metro train killed around 35 people and were claimed by the self-proclaimed Islamic State group.
But Ukraine's SBU state security service chief Vasyl Grytsak told reporters a possible Russian role could not be ruled out.
"I do not make unsubstantiated statements and affirm anything," Grytsak said in televised comments.
"But I would not be surprised if these acts of terror in Brussels have a Russian trace."
"SBU chief Grytsak, who made the announcement about Russia's involvement in the Brussels terrorist attacks, is a moron," Medvedev wrote on Facebook.
Relations between the two ex-Soviet neighbours have been frozen since Russia's March 2014 annexation of Ukraine's Crimea peninsula and the subsequent outbreak of a pro-Moscow eastern separatist revolt.
Russia denies Ukrainian and Western charges of sparking the conflict in reprisal for the February 2014 ouster in Kiev of the country's Kremlin-backed president.
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