He made a fresh appeal for anyone who was walking in the area at that time and may have seen the offender return to the scene "feeling remorseful'' - to contact the police.
But he discouraged people from putting up reward money to assist the police.
"At this stage we are only in day two of the operation and the risk we run by taking money and putting it out there for reward is someone tries to collect that reward and gives us a line of inquiry that may not be somewhere we need to go.''
Police had not yet interviewed the girl, whose condition was improving.
"When you see this little 5-year-old who has come to New Zealand with her family at Christmas time and has just been viciously attacked it does affect the guys who are working on the case.''
Bay of Plenty Police District Commander Glenn Dunbier said the girl's parents had remained "remarkably strong'' and were helping police as much as they could.
They had been overwhelmed with support from the public, he said.
"The family are lovely people and their plans are to get their daughter well and move on.''
The family, from Europe, have received hundreds of messages and gifts from members of the public since the attack.
"For us, we want to get on with our daughter's recovery,'' said the parents, who wish to remain anonymous.
"Physically she is doing better and better. She started playing and drawing in her bed. We are very touched by the reactions of New Zealanders.
"This will still be a long journey for us and it will be made that much easier by the loving care and messages we've received from throughout New Zealand.''
Mr Dunbier also praised the Turangi and wider New Zealand community.
"The support from the Turangi community and from further afield has been amazing with significant offers of accommodation, money and gifts for the family.
"What we really need, however, is the phone call that identifies our offender.
The victim's mother was in an amenities block metres from the caravan when the attack happened.
She returned to find the caravan locked, and through a window saw a man on top of her daughter.
She ran screaming for her husband, who was working on a computer in the amenities block, and they found their daughter unconscious on the bed.
One man at the campground, who did not wish to be identified, told TVNZ: "She (the mother) came back with her partner and they sprinted up to the caravan and then the father came running out screaming `help, help, help' and that's when I ran to the caravan and found a young girl in her mother's arms covered in blood with a really swollen face.
"The screams that were coming from the parents' mouths were just the sort of screams you never want to hear.''
