It was reported that the children had suffered knife wounds while Mr Fuller had fallen from a cliff at a nearby quarry.
Mr Fuller and his three children had left their home at Milkwall, near Coleford, Gloucestershire, last Thursday.
Police later appealed for sightings of the four and said they were believed to have been travelling in an 11-year-old red Land Rover Freelander.
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."