Medvedev, who is currently the deputy chairman of Russia's Security Council, also warned Moscow's conflict with the West could escalate into all-out war.
His warning came after the US and Germany became the latest allies to let Ukraine's military use Western-supplied weapons to strike targets inside Russia.
"Russia regards all long-range weapons used by Ukraine as already being directly controlled by servicemen from NATO countries. This is no military assistance, this is participation in a war against us," Medvedev said.
"And such actions could well become a casus belli."
He said giving Kyiv permission by the Western countries to use provided long-range weapons and ammunition to strike targets inside Russia will escalate the Ukraine war to its final stage.
"Nobody today can rule out the conflict's transition to its final stage," Medvedev said.
He said it would be a "fatal mistake" on the part of the West to think that Russia is not ready to use tactical nuclear weapons against Ukraine.
He also spoke of the potential to strike unnamed hostile countries with strategic nuclear weapons. "This is, alas, neither intimidation nor bluffing," said Medvedev.
MP/PressTV