According to a statement posted on a website on Wednesday, the group said: "After granting the Russian government 48 hours to meet our demands and their failure to do so ... the Islamic court of the Mujahidin Shura Council ruled to kill them.
"And let them be an example for those who follow them and challenge the mujahidin and dare to step foot in the land of honour, Iraq."
The statement's authenticity, however, could not be verified, and it was unclear when the hostages might be killed.
It added that the Russian government "did not respond to our conditions for releasing its diplomats and gave no value to its citizens, only calling for their release while continuing its war against Islam and its people".
It said the decision to kill the four came "in revenge for our brothers everywhere with whose blood the Russians' hands have been stained" and would be "an example for those who might follow them and dare to defy the mujahidin [Muslim fighters]."
On Monday, the group said it was holding the four Russians and gave Moscow 48 hours to meet its demands.
The council is an umbrella body composed of al-Qaeda in Iraq and several other groups, which has pledged to continue the battle against US-led forces despite the killing of Abu Musab al-Zarqawi, the leader of Iraq's al-Qaeda.
The decision came "in revenge for our brothers everywhere with whose blood the Russians' hands have been stained"
Mujahidin Shura Council
On June 3, four Russian embassy staff were kidnapped when gunmen blocked their vehicle in a Baghdad district and a fifth embassy employee was shot and killed.
Chechen fighters on Tuesday demanded the release of the hostages.
Akhmed Zakayev, the exiled foreign minister in the Chechen rebel "government", denied any links to the Mujahidin Shura Council.
The Russian foreign ministry called for the captives' immediate release and said: "The abduction of citizens of a country that is energetically helping to restore peace in Iraq" cannot be justified.