He also demanded the immediate and unconditional release of all hostages in Iraq.
Annan "condemns in the strongest possible terms these heinous acts, which no cause can justify," he said, through a spokesman.
The four Russian diplomats were kidnapped June 3, following an attack on their car in the Mansour district of Baghdad. A fifth diplomat was killed during the abduction. A group with alleged ties to al Qaeda, the Mujahedeen Shura Council, eventually took responsibility for the kidnapping, and June 19 set a 48-hour deadline for the Russian withdrawal of troops from Chechnya.
The Russian Foreign Ministry confirmed Monday that the four hostages had indeed been killed, after the Mujahedeen Shura Council displayed footage on a Web site of three of the four hostages being beheaded.
Russia, which has a permanent seat on the U.N. Security Council, voiced strong objections to the U.S.-backed invasion of Iraq and has since distanced itself from the United States on how best to wage a war on terror.
In recent months, Russia has differed with the United States over the threat of sanctions against Iran for what Washington has characterized as Iran's determination to begin a nuclear weapons program and over whether to characterize the violence in the Darfur region of Sudan as genocide.
Notable deaths of 2014 [PHOTOS]