Police are hunting for a 21-year-old man after his mother, a man and young girl were found stabbed to death.
The bodies of Janet Jordon, 48, Philip Howard, 44, and six-year-old Derrin Jordon were found at their home in Didcot, Oxfordshire, on Saturday.
Det Supt Chris Ward said officers were continuing to search for Jed Allen in connection with the deaths.
There is no suggestion he is armed and some officers are carrying weapons for their own protection, he added.
The detective repeated his earlier plea for anyone who knows Mr Allen's whereabouts to come forward.
Mr Allen, who has a distinctive black widow spider tattoo on his left hand, is described as white, about 6ft (1.8m) tall and stocky.
He is known to the police and members of the public have been warned not to approach him.
Although post-mortem examinations are yet to be carried out, police revealed the likely cause of death of the victims was stab wounds.
"This is a tragic incident and our thoughts are with the families of Janet, Philip and Derrin," said Det Supt Ward.
"It is vital that we trace Jed Allen and I would urge anyone who has any information about his whereabouts to contact police via the 101 number.
"If you see Jed please do not approach him, instead call 999 immediately."
Officers earlier cordoned off Oxford University Parks as part of their search and were also seen to erect a forensics tent.
Police said the search for Mr Allen, who formerly worked as a university groundskeeper at the park, was "intelligence led".
BBC South reporter Ben Moore said two more vans full of officers, some of them armed, had arrived at the site on Sunday evening to continue the search.
The victims' bodies were found in a house in Vicarage Road at about 20:20 BST on Saturday after police were alerted by concerned neighbours.
A number of people have visited the scene to leave floral tributes.
One tribute attached to a bunch of flowers read: "You are my family and always will be. I will miss you all each day. You have all left a massive void in my heart which will never be filled.
"I love you all so much, Jan, Phil and my Dezzy Doo."
Earlier, resident Sheila Welch said the family had only lived in the house for a couple of months and "always looked so happy".
Ms Welch said she was first alerted when police descended on the quiet residential road, adding there were "just sirens and police cars".
"All I can say is that I am very upset - it is all very traumatic," she added.