Detectives launched a murder investigation after the bodies of a man aged 38, a woman aged 37, and a teenage girl aged 15, were discovered at Glin Ree Court in Newry, Co Down, at around 11am on Thursday, police said.
It is understood they died in a violent way and one line of inquiry is a double murder and suicide.
It is also understood that the three were known to each other.
Police are not seeking anybody else in connection with the deaths.
Officers were called by a concerned member of a family worried they had not been in contact with a family member for several days.
Police forced entry to the building and found the bodies inside.
Local representatives have said at least two of the victims may be foreign.
Flowers carried by members of an emotional family arrived at the scene on Thursday evening.
Detective Superintendent Jason Murphy said: “I do not believe that anybody else was involved in the deaths of those three individuals and I am not currently seeking anybody else in connection with their deaths.”
He added: “At this time, the three have not been formally identified and cause of death has not been established.
“Our investigation is ongoing at present and our thoughts at this time are very much with the loved ones of those who have died.”
In reference to the victims’ identities, SDLP Assembly member Justin McNulty said: “There is an international dimension.”
A woman visited the cordon with a child who carried a bunch of flowers but they were not allowed into the sealed-off area.
Officers attended the scene and police tape marked the area preserved for forensic investigation in front of whitewashed flats.
Newry is close to Northern Ireland’s border with the Irish Republic.
Mr McNulty added: “This community is in shock and a dark cloud hangs over Newry this afternoon. My thoughts and prayers are with the families of the deceased.”