More than 2,000 people signed a petition on Change.org that sharply criticized the Cincinnati Police Department and the zoo for putting down the animal and called for the child's parents to be "held accountable for their actions of not supervising their child."
Cincinnati police on Sunday said the parents had not been charged, but that charges could eventually be sought by the Hamilton County Prosecuting Attorney. A spokeswoman for the prosecutor did not immediately respond to a request for comment.
Authorities did not identify the child or his parents. The family could not be reached on Sunday.
A Facebook page titled "Justice for Harambe" had more than 3,000 likes by Sunday afternoon, a day after the 400-pound (181-kg) gorilla was shot dead about 10 minutes after encountering and dragging the child. The animal, named Harambe, was a Western lowland gorilla, an endangered species, and the zoo said it had intended to use him for breeding.