The confirmation, in a statement on Monday, came a day after the Mujahidin Shura Council, an umbrella organisation linking seven groups including al-Qaida in Iraq, said that it had killed the four men who were seized this month.
The group has posted a web video on a website that frequently airs messages from such groups, showing the killing of three of the four Russian embassy workers abducted earlier this month in Iraq.
The one-and-a-half-minute video showed two blindfolded men beheaded and the shooting of a third man.
"God's verdict has been carried out on the Russian diplomats ... in revenge for the torture, killing and expulsion of our brothers and sisters by the infidel Russian government," the statement said.
The group had demanded that Russia should pull out its soldiers from Chechnya and release all Muslim prisoners.
The four Russians were abducted on June 3 after an attack on their car in Baghdad's al-Mansur neighbourhood.
A fifth Russian was killed in the incident.
The web posting showed the four men appear on camera, one at a time, staring ahead and speaking in Russian. Then the camera cuts to the killings.
The footage of the killings is
The posting was stamped with the logo of al-Qaeda. The men speaking into the camera is dated June 13, but the footage of the killings is undated.
The captives included the embassy's third secretary, Fyodor Zaitsev, and three other staffers: Rinat Agliulin, Anatoly Smirnov and Oleg Fedoseyev.
When the Mujahidin Shura Council posted a recent statement saying it had decided to kill the Russians, one of the hostage's sister, a Muslim, made an impassioned plea for the men to be freed.
"I beg you to pardon them and release them. You are Muslims, and Islam, before anything else, is a religion of peace and justice," Aliya Agliulin, sister of hostage Rinat Agliulin, said on Aljazeera television on June 21.
Videos of beheadings were an early signature of the Iraq insurgency, as well as a grisly trademark of tapes produced by the late Abu Musab al-Zarqawi. But such graphic images had become rare in the past year.