Police found the dead bodies of the three with bullet wounds in a house near the city of Malaga on Spain's Costa del Sol and initially said they were all British.
A Civil Guard spokesman told AFP however that they were a mother aged 54 and a daughter aged 28, both of Irish nationality, and a father of 56 who was a British passport-holder born in Kenya.
They had been living in the house for seven years, added the spokesman, who asked not to be named.
He also declined to name the family members, saying that their details had been passed to the British and Irish embassies in Spain.
Police sealed off the yellow villa and its garden with palm trees and swimming pool in the Torrenueva district of Mijas, a town southwest of Malaga.
A Civil Guard source who asked not to be named told AFP on Wednesday: "An initial hypothesis is being considered that… the man killed the woman and then his daughter and then committed suicide."
Several Spanish media cited unnamed sources saying that the mother was disabled and the daughter had Down's Syndrome, but officials would not confirm this.
Media quoted officials and neighbours saying the family had been renting the house for several years.
Reports said the owner of the property had found the family there dead when he visited after not hearing from them for several weeks.
A spokesman for the British embassy in Madrid said: "We are aware of these reports and we are investigating urgently."