Officers responded to a call at Llywellen Court in Ballinteer shortly before midday and discovered a 37-year-old woman, an 11-year-old girl and a six-year-old boy dead in the property.
The house has been designated a crime scene and will undergo a technical examination. A State Pathologist also attended the scene.
The womanâs husband and childrenâs father has been in contact with the police and is said to be in a distressed state and given access to medical treatment.
According to The Irish Times, gardaÃ (Irish police) have not ruled out foul play in the death of the mother, Seema Banu, or her children, Affira and Fazan. A ligature and note were reportedly found and it is believed they were strangled.
Neighbours alerted the police about their concerns for the family, who had not been seen for several days. It has been reported that they had been dead for some time and the property was flooded after a tap had been left running.
Superintendent Paul Reidy, of Blackrock Garda Station, said the post-mortem results will determine the course of the investigation.
The family moved to Ireland from India earlier this year and were described by neighbours as a very private family who kept to themselves.
Residents in Llewellyn Court held a candlelit vigil on Wednesday night in honour of the victims, and expressed their grief and shock at the tragedy.
Irish broadcaster RTE reported that the gardaÃ are pursuing a number of lines of inquiry and have been carrying out house to house interviews in an effort to establish the movements of the victims in recent days.
In a statement, the force also appealed for members of the public not to circulate âuninformed and unhelpfulâ comments about the case on social media.