The bodies of Sam Fuller, 12, and his sisters Becka, aged eight, and seven-year-old Charlotte were discovered by police at a beauty spot in Shropshire on Monday.
It is believed they had been stabbed to death by their father Ceri Fuller, 35, a Huddersfield University graduate, who then fell to his death from a nearby quarry.
West Mercia Police have recovered a knife and one line of inquiry detectives are following is that Mr Fuller killed the children before taking his own life.
David Fuller – Mr Fuller’s father and grandfather to the children – released a statement yesterday on behalf of his and his daughter-in-law’s families through police.
“Ceri was a gentle, sensitive and intelligent man but also a very private one,” he said. “He loved his children dearly and they were such a focal point of his life.
“His relationship with each one of them was one of gentleness, involvement and attentive nurturing.
“Sam, Rebecca and Charlie were such charming individuals, brought up in an environment of love.
“We cannot begin to imagine what was going through the mind of this gentle man to drive him to such tragic actions.”
Police said that Mr Fuller, from Hereford, had asked to be left to grieve in peace.
Earlier, the children’s mother spoke of her devastation at the news.
Ruth Fuller, who had been married to Ceri Fuller for nearly three years, 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.”
West Mercia Police launched a murder investigation after discovering the four bodies on Pontesbury Hill on Monday following a tip off from a member of the public about a red Land Rover Freelander estate parked there which police in Gloucestershire had issued an appeal over as part of their missing persons inquiry.
The force described the deaths as a “tragic family situation” and are not looking for anyone else.
Detective Chief Inspector Neil Jamieson, who is leading the investigation, said: “I can disclose that a weapon has been recovered from the scene. #
“Officers involved in the search found a knife in the vicinity of where the bodies were found.”
He added: “One line of inquiry being considered is that the father took the children’s lives before taking his own.”
Mr Jamieson said the old quarry and surrounding woodland would remain cordoned off as officers continue a detailed search.
Police are also appealing for information about possible sightings of the vehicle, registration CK51 YUV, and its four occupants on Thursday, when the children and their father were reported missing.
Mr Jamieson said: “We believe this vehicle left Gloucestershire at some point last Wednesday evening or early Thursday morning and we are anxious to establish its movements since then, especially in the Pontesbury area.
“We believe it was in the Leominster area at around midday on Thursday before making its way up towards Welshpool later that day.”
He said several people have already come forward with helpful information.
While police work continues in Shropshire, a team of West Mercia detectives have travelled to Gloucestershire to make further inquiries, including speaking to family members.
Mr Fuller married his wife Ruth in August 2009 and neighbours said the family had lived in their cream pebbledash semi-detached home in Station Road in the village of Milkwall for about a year.