A spokesman said Monday a 54-year-old man in hospital in critical condition is their prime suspect.
Three people are dead, including the man's 13-year-old daughter, his ex-wife and her new boyfriend.
The suspect's eleven-year-old daughter remains in critical condition in hospital stemming from the incident on Saturday night.
Police say the father is not in any condition to meet with investigators, who believe a possible love triangle may be behind the deaths.
Police have identified the dead found outside a home in St-Croix as Benoit Daigle, 39, and Nancy Samson, 44.
The young girl who perished in the home in St-Isidore is Medora Godin, 13. She and her sister were found in a home, about 70 kilometres from where the first two bodies were discovered.
The towns are both located in a region south of Quebec City.
Autopsies are scheduled to be performed later today on the deceased.Suggest a correction