The family has thanked police, St John Ambulance and Waikato Hospital who have cared for their daughter. The family wish to remain anonymous.
Meanwhile, appalled Turangi community members are offering to put up their own money as a reward for information leading to the arrest of a man responsible.
Police say the investigation is ongoing and that offers of money, while generous, needed to be given careful consideration.
"Offers of money can result in misleading information and it is vital that the investigation team remains focused," said Detective Inspector Mark Loper.
The children and their parents are visiting from Europe and the mother was in an amenities block metres away 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.
She was flown to Waikato Hospital, where she had four hours of surgery.
Neighbours who live across the road from the holiday park told the Herald that the Mongrel Mob were out in "full force" on Wednesday night.
Gang members were partying at a home in nearby Raukura St and the residents saw a blue or grey van and black hatchback vehicle parked outside the reserve next to the camping ground between 9.30pm and 10pm.
The neighbours did not recognise the occupants as members of the local Mongrel Mob chapter, but at least two wore patches and appeared to be having a meeting.
Another man joined the group after walking through the reserve.
"Police are aware of some house parties that were held in Turangi on Wednesday
night and the people at those parties will be spoken to as part of the wider area canvass that is underway.
"Some information has been coming in from the public to the Police and is being followed up, but Police still want to hear from anyone with even the smallest piece of information that might be useful."
Loper said the assault was one of the worst on a child he had seen in his 28 years in the police.
"The attack was brutal, on a young defenceless child who should have been spending Christmas on a dream holiday with her family. Her parents are absolutely distraught."
But he said police were planning to interview known offenders living in the area, and a team of 30 staff from Taupo, Rotorua and Waikato were examining the crime scene for fingerprints and DNA.
Police were also visiting local businesses and taking CCTV footage from Wednesday evening.
The girl's injuries were "significant and heart-wrenching", he said.
The girl is this morning in a stable condition in Waikato Hospital.
Club Habitat manager Sylvia George said she felt sick that the assault had happened at the camping ground, but people often walked through the property as it was a shortcut between State Highway 1 and the town.
"I've been working here for quite a while and this is the first thing we've kind of had ... someone brutally attacked."
The family had booked to stay for one night and planned to walk the popular Tongariro Crossing in National Park.
Ms George said four other campervans were parked near the caravan, but only one camper had heard the screams of the mother.
Turangi locals have condemned the attack. Tongariro Chartered Club bar worker Terry Downs said the town wanted the person to be found and justice to be served.
"The town is appalled by it. They will be crying for blood."
Turangi Returned and Services Association president John Smith said everyone at the club "is just disgusted".
Mr Loper asked the community to focus on the time between 10pm and 10.45pm on Wednesday and report any activity around the park.
"It doesn't matter how irrelevant the piece of information may seem, let us judge its importance," he said.
"It is vital that we catch the person responsible for this attack sooner rather than later."
Turangi cousins Kohine Hamilton and Bobby Jade Wilson said the attack was shocking.
Ms Wilson, who has a 3-year-old son, planned to keep the doors locked last night.
The cousins said Turangi was usually fairly safe because it was such a small community.
CAN YOU HELP?
Call the Taupo police on (07) 378-6060 or Crimestoppers anonymously on 0800-555- 111.
A trust fund has been set up at Westpac Bank, account number 03-1555-0150947-00 under the name "Operation Turangi".
Gifts have been coming in and are being accepted at collection points at Hamilton Police Station and Waikato Hospital. Given the family will travel back to Europe soon, some will have to remain in New Zealand. They will be donated to other sick children in Waikato Hospital.
