The family of three children apparently killed by their father "cannot begin to imagine" what was going through his mind.
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 yesterday.
It is believed they had been stabbed to death by their father Ceri Fuller, 35, 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 on behalf of his and his daughter-in-law's families through police.
"The Fuller and Tocknell families are devastated by this tragedy," Mr Fuller said.
"Ceri was a gentle, sensitive and intelligent man but also a very private one. 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.
"We would ask all to respect our privacy at this time while we try to come to terms with this terrible loss."
Police said that Mr Fuller, from Hereford, had asked to be left to grieve in peace.
Earlier today the children's' mother spoke of her devastation.
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 at the Poles Coppice on Pontesbury Hill.
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.
"It will now be forensically examined.
"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 of the area.
Post-mortem examinations will be conducted this afternoon by a Home Office pathologist and may not be concluded until tomorrow, the detective confirmed.
Police are appealing for information about possible sightings of the vehicle and its four occupants on Thursday.
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 that would help police track the vehicle's movements.
"This is in response to our appeals and we are grateful for their assistance," he said.
"However, I am still urging people to call Shrewsbury police station on 101 or our other number, 0300 333 3000, with any details which could help the investigation."
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.
"We are working very closely with our colleagues in Gloucestershire to try to establish the full circumstances leading up to this tragedy," Mr Jamieson added.
Officers found the bodies of the Fuller children shortly before 10am yesterday. The family Land Rover Freelander was discovered nearby.
University graduate Mr Fuller and the children had left their home at Milkwall, near Coleford, Gloucestershire, last Thursday.
Becka and Charlie were pupils at St John's Church of England Primary School in Coleford, which older brother Sam had also attended before moving to secondary school.
Headteacher Jan Wagstaff said: "Rebecca and Charlotte were absolutely delightful children and a pleasure to have in school.
"Sam was also a pupil here before he moved on to Lakers. He was a lot of fun and always had a ready smile. They will all be very sadly missed.
"Our thoughts and prayers are with their family."
Alison Elliott, head of Lakers School in Coleford, added: "We are desperately sad to hear the family are having to face such a dreadful situation.
"Sam was a well loved member of our extended family here at Lakers. Our thoughts are with the family at this very tragic time.
"We have arrangements in place to support students, staff, friends and family at this very difficult time."
Mr Fuller married his wife Ruth in August 2009 and neighbours said they had lived in a cream pebbledash semi-detached home on Station Road in the village of Milkwall for about a year.
Neighbours said the family "kept themselves to themselves" but spoke of their shock.
Janice Ayres, who lives next door to the Fuller family, said: "Very, very sad, I just cannot say any more.
"I didn't even know her name (mother of the children). I have children of my own and I would just be devastated.
"I am surprised. They kept themselves to themselves. It's so sad for three young children.
"Being out at work all day you don't really know your neighbours. We would speak if we saw each other in the garden but we never socialised together.
"They were no trouble at all. They've lived here about a year and as far as I know they bought the house as we knew the man who lived there before and he was selling it.
"It is dreadful really to think about it. It's the way life is these days. You just live your own life."
Another neighbour, who did not wish to give their name, added: "They hadn't lived here all that long. They kept themselves to themselves."
Mr Fuller worked as a production supervisor at the Lydney-based Glatfelter paper mill, having joined in 2002.
According to his LinkedIn profile, Mr Fuller was educated at Whitecross School in Lydney before taking A-levels in physics, chemistry, biology and general studies at the Royal Forest of Dean College.
He then completed a BSc in molecular and cellular biology at the University of Huddersfield, graduating in 2001.