The police said the family was murdered by "unidentified miscreants" on Monday night.
A 35-year-old school teacher, his pregnant wife and their six-year-old son were hacked to death in their home in West Bengal's Murshidabad district on Tuesday.
The bodies of Bandhu Prakash Pal, a 35-year-old primary school teacher, his wife Beauty, 30, and young son Arya were found in different parts of their blood-splattered home in Jiaganj, about 210 km from Kolkata, around noon on the day Vijayadashami and Dussehra were being celebrated.
The woman was reported to be pregnant.
There have been no arrests in the case so far but the police say they are investigating several angles. One of their theories is that all three may have been drugged before being knifed.
The murder has taken a political turn with the BJP and its ideological mentor Rashtriya Swayamsevak Sangh (RSS) claiming Bondhu Pal had recently joined the RSS.
The news as well as graphic photos and a video of the bodies are in wide circulation on social media.
BJP spokesperson Sambit Patra was among those who tweeted the video - with a warning about its gruesome nature - questioned the law and order situation in Bengal. "This has shaken my conscience ...a RSS worker Bandhu Prakash Pal, his eight months pregnant wife and his kid were brutally slaughtered in West Bengal's Murshidabad Not a word by the liberals Not a letter by 59 liberals to Mamata Nauseating Selectivism," he tweeted.
The family had reportedly moved into the area two years ago.
The police said the family was murdered by "unidentified miscreants" and dismissed any communal or political twist to the killings. Officers said the family's property matters and personal relationships were being examined.
The brutality of the murders, executed with a sharp weapon, has stunned the town.
The crime was revealed when neighbours, concerned about the family's absence at the puja pandal on Vijayadashami, went to their home and found the door bolted from inside.
"The locals informed the police and the bodies, lying in a pool of blood, were found," said an officer, according to the Press Trust of India.
Bandhu Pal's cousin Sujoy Ghosh was quoted telling news agency ANI that he had shifted to Murshidabad for his son's education. "We do not know if they had any problem with anyone," he said.
ANI also quoted RSS West Bengal secretary Jishnu Basu as saying that Pal was an RSS worker and had been recently associated with a 'weekly milan (meeting)'.