News NI understands the man who died was from Guinea-Bissau, but had lived in Northern Ireland for more than two decades.
Speaking to the media on Monday, PSNI Supt Peter Stevenson said police received a report on Saturday morning from a member of the public about an ongoing disturbance at the house.
“Officers arrived short time later and discovered the body of a man, aged 61, his 48-year-old wife, who sustained non life threatening injuries, and their severely injured eight-year-old daughter,” Stevenson said.
He said officers immediately commenced first aid on the woman and girl.
“I am in no doubt their quick actions gave the young girl a fighting chance at survival,” Stevenson said, adding that she is now in a stable condition in hospital.
The Northern Ireland Ambulance Service (NIAS) said they received a 999 call at 11:08 on Saturday, following reports of an incident.
They dispatched a helicopter crew, three emergency crews, one advanced care paramedic, two ambulance officers and one HART (Hazardous Area Response Team) crew to the scene.