The statement was made in a letter from Putin to Iranian President Masoud Pezeshkian, published by the Kremlin.
China's Foreign Ministry has also condemned the killing of Ali Khamenei, calling it a violation of Iran's sovereignty.
On Saturday, the Russian government condemned the attack on Iran as a "dangerous adventure" that could lead to a "catastrophe" for the entire region.
Russian Foreign Minister Sergei Lavrov also spoke with his Iranian counterpart, Abbas Araghchi, on Saturday.
Russia and Iran signed a strategic partnership agreement last year, including measures to strengthen military cooperation.
