A vehicle carrying pro-Moscow policemen came under attack after it hit a landmine planted by separatists in southern Chechnya on Monday, said security officials on Tuesday.
Separatists then fired on the vehicle, killing at least three servicemen.
Another eight Russian interior ministry troops, called as reinforcements, were killed when they hit a landmine and came under rocket attack. Another soldier is said to be missing.
Also on Monday, one Russian soldier was killed and two were wounded when a Russian military truck hit a landmine in the Chechen capital Grozny, said a Chechen official.
It was the worst single loss for Moscow forces since 26 March when 10 soldiers died after an officer drove on to a minefield next to a checkpoint.
Monday's attack came a week after Chechnya's pro-Kremlin president Akhmad Kadyrov was killed when a bomb detonated at a military parade in Grozny. Kadyrov was the Kremlin's main ally in Chechnya.
In 2000, Russian troops ended a short-lived independence for Chechnya, won after a war from 1994 to 1996. Moscow poured troops into Chechnya in 1999, triggering an uprising for independence.