One of the bodies was found lying on the floor and the others hanging from a railing attached to the ceiling, media reports said.
Seven of the victims are women, including three teenagers, while four are men.
The family ran a grocery shop and plywood business out of their double-storey home in Sant Nagar, in north Delhi's Burari's area. Two of the deceased are minors, they said.
'It is a tragic incident. Chief Minister Arvind Kejriwal and Delhi BJP Chief Manoj Tiwari visited the spot.According to police, they were initially informed by a neighbour that six to seven people have committed suicide. The incident came to light when a neighbour went to the house to call the family head with whom he go for morning walk. Police said the two gangs are headed by men whose enmity goes back to 2013.
The police are not certain if the deaths were a result of suicide or murder.
Indian TV channels broadcast interviews with neighbors who said the family did not have any discord among themselves.
The police is investigating the case from all possible angles, Joint Commissioner of Police, Delhi, told ANI. 'We can't rule out anything, ' he said.