Russian news agencies on Thursday reported that the fighters were killed in three separate shootouts in the southern Vedeno, Shali and Shatoi regions.
Colonel Ilya Shabalkin, a spokesman for the Russian forces in the North Caucasus region, said three people were also injured when a bomb exploded while being defused by Russian soldiers.
Chechen separatists seeking independence for the region from Moscow’s rule have been fighting Russian troops in a war that has cost tens of thousands of lives.
Fighting first broke out in the mid-1990s when the mainly Muslim region tried to break away from Russia.
Moscow sent in troops to the Chechen capital of Grozny again in 1999, but the second separatist war in a decade in the region has since degenerated into a brutal guerilla conflict.