Andrew McGowan, 35, of Cockburn Street, Dingle, pleaded guilty to the charge at Liverpool and Knowsley Magistrates' Court.
The toddler suffered serious head and body injuries in the "horrific attack" in a garden on Sunday.
McGowan was bailed until 6 June when he is due to be sentenced.
The injured child's father wept as he attended court.
The dogs also hurt a 57-year-old woman, who tried to rescue the girl in the garden on Cockburn Street.
The girl, who cannot be named for legal reasons, was taken by air ambulance to Alder Hey Children's Hospital after the alarm was raised at about 15:40 BST.
Neighbours said they heard the girl screaming and shouts of: "The dog's got the baby! The dog's got the baby!"
One neighbour described the attack as "shocking", adding there had been previously "no problems at all with any of the dogs".
Five dogs and six puppies were seized after the attack, two of which were put down.
American bully dogs are not a banned breed, police said.
Source: United Kennel Club
A man has admitted owning four dogs that were dangerously out of control after an attack left a two-year-old girl badly injured.