Six people in the eastern state of Orissa have already been arrested, but police believe more people were involved in the crime.
The bodies of Mangri Munda and her children were found in a well near their home on 26 January.
"Witch hunts" targeting women are fairly common in parts of India.
Senior police officer Kavita Jalan told the BBC that the main accused, who has been arrested, claimed to be a "witch doctor".
He had accused Ms Munda and her children, who lived in a tribal settlement in Sundergarh district, of "casting spells" on another family in the village.
On 25 January, a group of men broke into Ms Munda's home late at night when she and her two sons and two daughters - aged one, four, seven and 12 respectively - were asleep. They attacked them with wooden sticks and an axe before dumping their bodies inside a well.