One separatist was also reported killed during a clash between rebels and Russian soldiers in the region of Urus-Martan, southwest of the capital, Grozny, that also left three soldiers injured, the official in Chechnya's pro-Moscow administration said.
In another incident, he said, one Russian soldier died and six others were injured after their truck exploded on a mine near the village of Ulusker in the southern region of Shali.
Four soldiers were killed and seven injured in other attacks throughout the mountainous republic, during which Russian positions came under fire 17 times.
Separately, one Russian soldier died after being shot by a fellow serviceman in what authorities described as a careless handling of arms.
Separatists have been fighting pro-Russian forces in Chechnya for more than five years, the second such war in less than a decade.