Three people were beaten to death in Seraikela district on Thursday morning and three more were killed in Jamshedpur district in the evening.
A senior police official told BBC Hindi that the incidents happened because of "rumours that a child-kidnapping group was active in these areas".
Police have not yet arrested any suspects in the two cases.
It is not clear when and how the rumours started. But RK Malik, a spokesperson for the state police, said people had become increasingly worried by them.