Ruth Fuller, the mother of the three children apparently killed by their father, has released a short statement through Gloucestershire Police.
Mrs Fuller said: "I don't have the words to describe how I feel at the moment. All I would ask is that I be left alone to grieve for my family."
Earlier on Tuesday, police announced they were investigating the deaths of the children and their father after the bodies of Sam Fuller, 12, Rebecca, eight and Charlotte, seven, were discovered in woodland in Shropshire on Monday.
The Birmingham Mail reported that the three children all died from stab wounds, and that their father, 35-year-old Ceri Fuller, died after apparently falling from a cliff at a quarry in the area.
Police investigating the murder of three siblings have revealed they found a knife at the scene.
Detectives have yet to officially reveal a cause of death but they have announced that a murder inquiry has been launched and that they are not looking for anyone else.
Mr Fuller is said to have left his Milkwall home with his children on Thursday, and their bodies were found shortly before 10am on Monday.
Tributes have been paid to the children, with the girls' headteacher saying they were "absolutely delightful children and a pleasure to have in school".