The announcement was made in a statement posted on the Internet. The authenticity of the statement could not be verified.
The Mujahedin Shura Council has demanded Moscow to pull out of Chechnya and free Muslim prisoners from Russian jails. The separatist government in Chechnya has denied any connection to the group and called for the release of the hostages.
The four Russian Embassy employees were abducted on June 3 in Baghdad. A fifth was shot dead.