Enrique Cano, 61, Concepcion Bautista, 50, and a 14-year-old daughter died Dec. 14 at their home in Alcala de Guadaira near Seville, ThinkSpain reported Saturday. Another daughter, 13, survived.
Authorities have ruled out homicide or suicide, officials said. Relatives say reports the family was raiding trash cans for food because of financial problems are untrue.
The couple and their older daughter ate the same dinner on the day of their death, marinated rock salmon, while the 13-year-old had a ham sandwich.
Experts identified the cause of death as aluminium phosphate, a chemical used to kill rodents. They said it is quickly fatal even in small doses if it is inhaled or eaten.
They have been unable to determine how the family consumed the poison.