The four Russians were kidnapped in Baghdad on June 3.
A group linked to Al-Qaeda posted footage on the Internet on June 25, saying it killed the four hostages.
The hostage takers had given Russia a deadline to withdraw its forces from Chechnya and free Muslim prisoners from Russian jails.
The video purportedly shows the execution of three them. An accompanying statement said the fourth employee had also been killed.
Russian officials initially questioned whether the video was actually of the embassy employees.
"The Council of Muftis of Russia strongly condemns the execution of the Russian diplomats in Iraq and declares that this evil act has neither religious nor human justification," Council of Muftis Chairman Ravil Gainutdin told reporters in Moscow. "On this difficult day, at this hour, we say 'no' to evil doing, 'no' to extremism and terrorism."