Thames Valley Police said officers were called to a house in Broadlands, Netherfield, Milton Keynes, by the ambulance service just after 5pm on January 31.
The youngster, who died at the scene, has been identified as Alice Stones.
The force said: “There has also been a large amount of speculation around the breed of the dog.
“Although we are not in a position to confirm the exact breed of the dog due to the requirement for further testing, we are able to confirm that the dog is not a banned breed.
“We’d also reiterate our ask that the privacy of Alice’s family is respected at this extremely difficult time.”
The animal, which was a family pet, was put down by police.
Last week around 100 people turned out to a vigil that had been organised at Grand Union Vineyard Church, Netherfield Campus, across the road from the house.
Prayers were said for the family as people gathered, holding candles, in the darkness in a green space at the rear of the place of worship.
There were moments of reflection as music was played over speakers, including Amazing Grace and Over The Rainbow
Among the floral tributes left to the youngster, one of them read: “Alice!! Fly high with the angels little one. The whole community will miss your smile. Our thoughts are with the whole family, especially her mum.”
Neighbour Rita Matthews, 36, said she would see Alice while walking her own daughter to school and described the youngster as a “happy little girl, very happy”.