"I will be brief: Ukraine is on the brink of civil war, it's frightening," the country's former president was quoted as saying by Russian news agencies.
Medvedev expressed hope that Ukraine's "de-facto authorities" would be reasonable and not to allow "this sort of terrible turmoil."
Russia does not recognise Kiev's pro-Western authorities who came to power after a popular uprising ousted Moscow-backed President Viktor Yanukovych.
Medvedev, who ruled Russia between 2008 and 2012 and stepped down to allow his mentor Vladimir Putin to return to the Kremlin for a third term, also took issue with the Ukrainian authorities' appeal to bring United Nations troops to help calm tensions.
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He also reiterated calls for the United States and the European Union to follow up their pledges of support with real action, saying promises of jam tomorrow were no longer enough for the ex-Soviet's troubled economy.
"All those who say that it is necessary to help Ukraine should finally do something for Ukraine," Medvedev said.
"I mean both our European partners and our partners across the ocean. Let them give at least a dollar. Endless promises: we will give a billion, we will transfer five billion. Let them give something."
"There are such calculations, these are not phantom figures, they are real figures."
His Belarussian counterpart Mikhail Myasnikovich for his part said Ukraine would be able to solve its problems alone.
"We believe that they will sort it out independently and solve the difficult tasks the country is now facing," he was quoted as saying.