They then entered the house and found the bodies of three young children, two boys and a girl.
A female relative in her 40s was at the scene and is now being treated in Tallaght University Hospital.
"Gardaí are now investigating the circumstances of their unexplained deaths".
It is believed the family moved to Newcastle about a year ago.
The estate where the young family lived, Parson's Court, is made up of both houses and apartments.
Associated Press maintains its still not clear to gardai just how the children had died when they attended the scene.
The children are brothers and sister Conor, aged nine, Darragh, aged seven, and Carla aged three.
There, they discovered the bodies of the three children. She is receiving medical treatment in Tallaght University Hospital.
The results of the post mortem will determine the cause of death of the 3 children.
The scene is now being examined by members of the Garda Technical Bureau.
A family liaison officer has also been appointed and is in contact with the father and the extended family.
The house has been sealed off for a forensic examination.
Councillor for Fine Gael Emer Higgins described the events as an "unimaginable tragedy".
She said: "My thoughts are with everybody impacted".
She said: "Gardaí are now attending the scene of an incident at a domestic house in Newcastle, Co".
Anyone with information is asked to contact Clondalkin Station 01 6667600 or the Garda Confidential Line 1800 666 111.