The deaths of the sibling are being treated by Gardaí as "sudden" and "unexplained".
The bodies were found in a house at Parson's Court in Newcastle village, northwest of Rathcoole, last night.
They have been named as Conor ( 9), Darragh (7) and Carla (3) McGinley.
The bodies of the three children have since been removed to the city morgue.
Police sources said they had found no evidence anyone else was in the house when the children died.
Democrats urge Republican ‘courage at Trumps impeachment trial
Senator Shelley Moore Capito said Friday she hasn't made up her mind about witnesses. Saturday's opening arguments begin at 10 AM ET and are expected to last three hours.
Mr McGinley has released a photo of himself with his three children.
Gardai said a family liaison officer was in contact with their father Andrew McGinley and the extended family.
The Garda Technical Bureau has also been alerted and a detailed forensic examination in the area was being carried out.
According to The Sun, Gardai suspect the three children may have been "drugged" or "poisoned".
Irish police are awaiting the results of post-mortem examinations after the bodies of three children were found at a house in Newcastle, County Dublin.
Police seeking warrant for Antonio Brown’s arrest for battery and burglary
He played one game for the New England Patriots but was released after sexual assault allegations surfaced against him . Public information officer Christian Lata told USA Today on Wednesday that Brown had "locked himself in his house".
The local councillor, Emer Higgins, described the events as an "unimaginable tragedy".
'My thoughts are with everybody impacted, ' said the Fine Gael representative. She is receiving medical treatment in Tallaght University Hospital.
Assistant State Pathologist Margot Bolster has attended the scene.
Gardaí are appealing for witnesses or anyone with information to contact the incident room at Clondalkin Garda Station on 01-6667600.
Anti-government protests escalate in Lebanon
Security forces and the military were girding themselves for more violence, following protester calls for more rallies on Sunday. The Internal Security Forces said 142 police were injured.