Police were searching for the owners of the elephants and trying to establish what caused the violent behavior, rare among tamed elephants.
The attacks occurred Wednesday in an area bordering India's Assam and Mizoram states, said Gautam Ganguly, a senior government official in the area.
The two elephants, a male and a female, ran through at least five villages, trampling anyone who got in their way before crossing into the neighboring state of Mizoram, where police were called in.
"Men of the Mizoram police finally gunned the elephants down after dusk," Ganguly said.
Angry villagers protesting the lack of protection burned down the local forestry office.
Local government officials later announced that the families of the dead would receive $1,250 in compensation.
The region is home to some 5,000 wild Asiatic elephants and conflicts between the elephants and humans have been on the rise due to constant encroachment on the elephant habitat. However, attacks by tamed elephants are extremely rare.