Bay of Plenty police spokeswoman Kim Perks said all four dogs had been destroyed by a vet.
Police have completed a scene examination and an investigation would continue today.
Ms Perks said the dog owners were co-operating fully with the investigation.
Whakatane District Mayor Tony Bonne told Radio New Zealand this morning that some dog breeds should be banned.
"I believe there's some dogs out there that have got that have got that fighting technique streak in them and shouldn't be around."
The Government had considered a ban in the past but had decided against it, he said.
Mr Bonne said like most communities, his had problems with unregistered dogs. But the dogs in yesterday's attack were registered and microchipped.
"The owner obviously was a responsible dog owner and was devastated. But there are breeds of dogs that are in New Zealand which I personally don't agree with, but the government of the day has allowed them.
"So as long as the dog owners are responsible with them - and this attack happened on the property, so it was not on the streets - really it's one of those very unfortunate incidents."
Mr Bonne said it was sad the girl's family had only just moved to Murupara before the attack.
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"When somebody's just moved to town, it will be absolutely devastating for them, for the family."
Murupara community board chairman Jacob Te Kurapa told Radio New Zealand the family had moved to Murupara six weeks ago and were looking forward to a new life in New Zealand and the town.
A law change in 2003 banned imports of several breeds of dog and gave the Government power to ban imports of other breeds in the future.
The four banned breeds were the American pitbull terrier, dogo Argentino, Brazilian fila, and Japanese tosa.
Another breed, the perro de presa canario, was banned by an order in council agreed by Parliament in 2011.
Orders in council to ban further breeds can be recommended by the Minister of Local Government after consultation with local government, animal welfare organisations, dog clubs and veterinary practices.