Zainabou Drame remained in critical condition in a medically induced coma with many surgeries and much therapy ahead of her, they said.
"She's currently resting peacefully, but I hope she can survive these next weeks," family member Leslee McElrath said.
"She liked to play with her little brother. She liked to smile. She was learning to read. She was a normal 6-year-old," McElrath said.
Cincinnati Police have said the dogs chased after Zainabou, dragged her for a bit and then attacked her last Wednesday.
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"She is lying there -- her face is swollen almost beyond recognition -- I thank God she is still here," Gina Tyus told the newspaper.
Police arrived to the scene quickly, and squad car dashboard camera footage released on Friday shows officers running toward Zainabou as the dogs hover above her.
The dogs scurried, and officers can be seen firing shots in their direction. Both dogs were killed by the gunfire.
Zainabou's family members appealed to dog owners to be more cognizant of what their pets are up to.
One of the officers who responded to the attack told WLWT-TV that the scene was the worst thing he had seen during his nine years on the force.
"The image I will never get out of my head which was the child's head was in the mouth of the brown dog and he was thrashing his head back and forth," Officer Kyle Strunk said.