The three people shot dead in Co Fermanagh have been named locally as Vanessa Whyte and her children James and Sara.
They were shot during an incident in their home in Maguiresbridge, Co Fermanagh.
A man remains in a serious condition in hospital.
One line of inquiry being investigated by police is that what happened was a triple murder and attempted suicide.
Superintendent Robert McGowan confirmed that all four people were from the same household and suffered gunshot wounds.
The PSNI has begun a murder investigation and said detectives are “working at pace to determine the circumstances”.
A 999 call was made from the house at around 8am yesterday morning
Two of the victims, Ms Whyte, who was in her 40s, and one of the children, were pronounced dead at the scene on Drummeer Road.
The second child died later in hospital.
Police said they received a 999 called from someone inside the house appealing for help shortly before 8am yesterday morning.
Officers were despatched immediately from Enniskillen station around 13km away.
When they arrived at the property, they found four people inside with gunshot wounds.
St Mary’s Maguiresbridge Gaelic Football Club and St Patrick’s Hurling Club, based in the village of Lisbellaw, close to Maguiresbridge, said the three people who died were active members of both clubs.