Mikhail Kamynin said: "Moscow believes only productive and effective dialogue between all Iraqi forces, involving the international community and Iraq's neighbors, can bring the situation in the country back to normal."
Ramadan was executed early on Tuesday morning. On March 15, a court in Iraq confirmed the death penalty for one of Saddam Hussein's co-defendants for his role in killing Shias in 1982.
Initially Ramadan was sentenced to life, but the punishment was increased at an appeal.
Ramadan was the fourth former Iraqi official sentenced to death after overthrown Iraqi President Saddam Hussein, former Iraqi intelligence chief Barzan Al-Tiqriti and Avvad al-Bandar, the former head of Iraq's Revolutionary Court.