"The vehicle has since been spotted in the Shrewsbury/Welshpool area, but areas police suspect the family may be also include Barmouth and Harlech, in north-west Wales," a force spokesman said.
"Mr Fuller is described as being a white man, approximately five feet 11 inches tall, of stout build, with short strawberry blonde hair, and a stubbly beard.
"He wears glasses and a wedding band, smokes roll-ups and has a Celtic/tribal design tattoo on his upper arm/shoulder.
"Anyone who has seen the family or has information that could help locate them is asked to ring Gloucestershire police on 101 quoting incident number 62 of July 13."
The Birmingham Mail reported that the three children all died from stab wounds after being found in a wooded area in Pontesbury Hill, eight miles from Shrewsbury. The newspaper also reported that Mr Fuller has also died after apparently falling from a cliff at a quarry in the area.