The family who were found dead at their home in southern Spain have been named as Sheila and Philip Wood and their daughter, Sophie.
They had lived in the area for ten years and were well-known locally.
Shield Wood and her daughter both held Irish passports.
Mr Wood was a British national.
The Department of Foreign Affairs said it is in contact with family members in Ireland and providing consular assistance
It is thought the three died from gunshot wounds inflicted by one of the adults. A note was found at the scene.
Police are not looking for anyone else in connection with the deaths.
The bodies were found inside the apartment in Mijas, Fuengirola, by their landlord.
The Foreign Office in London said it was "liaising closely" with the local police and was ready to provide consular assistance.
Last night, a Guardia Civil spokeswoman said the family were renting the property where they were found dead.
"The latest information we have is that the owner of the house had not heard from the family for a few days and had not been paid," she said.
"He went to the house today and when there was no reply at the door, he went inside. Inside, he saw the man dead on the sofa and immediately called the Guardia Civil.
"When officers inspected the house they found the wife and the daughter dead in a bedroom."
Mijas is a popular town with a reputation for being family-friendly with its many cafes and restaurants.