They have been named as brothers Conor (aged 9), Darragh (7) and sister Carla (3) McGinley.
The discovery was made at Parsons Court in Newcastle on Friday night.
The post-mortems on the three children were completed by Assistant State Pathologist Margot Bolster at the Dublin City Morgue on Saturday evening.
Gardaí say interim post-mortem results are not being published for operational reasons - while they await further toxicology results.
A woman aged in her 40s, believed to be the children's mother, is continuing to receive medical treatment at Tallaght University Hospital.
Gardaí say they are continuing to investigate all the circumstances of these "unexplained deaths."
A family liaison officer has also been appointed and is in contact with the father, Andrew McGinley, and the extended family.
Forensics officers at the scene where the bodies of three children were found dead on Parsons Court, Newcastle in Dublin | Image: Sam Boal/Rollingnews.ie
The house at Parsons Court continues to be sealed off and examined by the Garda Technical Bureau.
Anyone with any information in relation to this incident is asked to contact Clondalkin Garda station on 01-666-7600.
Gardaí have said they are not looking for any other person in relation to this incident at this time.
The South Dublin Children and Young People's Service Committee (CYPSC) of Tusla says it has activated its critical response procedure.
It says: "The CYPSC, which is made up of statutory and voluntary services, has activated its critical response procedure and is assessing the risks to, and needs of the community during this difficult time for the community.
"We are aware that one support may assist one family, but the same support may not be best for another, and so the CYPSC is working to ensure tailored/appropriate supports will be available through schools, counselling services, family support services, local groups etc to support children and families through the days, weeks and months that follow."
