The Mujahedin Shura Council gave Moscow 48 hours to pull out of Chechnya and free Muslim prisoners or "take the consequences."
The group also claimed responsibility for the killing of a Russian Embassy employee on June 3 during the abduction of the four Russians.
The Mujahedin Shura Council today also claimed to have kidnapped two U.S. soldiers who were seized south of Baghdad on June 16.
The authenticity of the statements could not be verified, but they appeared on a website known for publishing messages from insurgent groups in Iraq.
Russian Foreign Ministry spokesman Mikhael Kamynin appealed to the kidnappers to immediately release the Russian citizens and ensure their safety.