Russian diplomat Vitaly Titov was killed during the attack on an embassy car in the capital of Iraq on June 3. The kidnappers seized Fyodor Zaitsev, third secretary of the embassy, and also diplomats Rinat Agliulin, Anatoly Smirnov and Oleg Fedoseyev.
Sergei Mironov said, "Talks are under way and we are searching for ways to resolve the problem."
"We are looking for new contacts and opportunities. The leadership of this country is making every effort to release its citizens," he said, condemning the crime as "inhuman".
Mikhail Kamynin, the official spokesman for the Foreign Ministry, said Wednesday that the Mujahideen Shura Council, a group linked to the al-Qaeda cell in Iraq that claimed responsibility for the abduction, had sentenced the diplomats to death.
The Foreign Ministry appealed again Wednesday for the immediate release of four diplomats, saying in a statement that they were "representatives of the Russian people, who have never waged a war against Islam anywhere."
Foreign Minister Sergei Lavrov said earlier that information about hostages had been coming in regularly and its reliability had been checked.