New York City police said a girl called to report the incident, which occurred in Far Rockaway, Queens, and said "one of her relatives was killing her family members."
Police told reporters that the 38-year-old suspect stabbed two police officers who went to the scene, one of whom shot and killed him.
She stated that the suspect had previously been arrested for an incident of domestic violence. The injured officers were taken to hospital for treatment.
Police said the four people stabbed to death were a 12-year-old boy, an 11-year-old girl, a 44-year-old woman and a man in his thirties. She said she found the 11-year-old in front of the house, while the other three were inside the bedrooms.
Police said a fifth man, a 61-year-old woman, was stabbed and was in hospital in critical condition.
Police said the suspect set fire to a sofa in the living room of the house, forcing officers to wait for fire crews to arrive before entering the house.