Police in the US may bring criminal charges over an incident that saw Harambe the gorilla shot and killed in order to rescue a 4-year-old boy who had fallen into his enclosure at Cincinnati Zoo.

Police are to investigate the circumstances around the shooting, and it is understood that Cleveland Police are taking a second look at possible criminal charges.

There has been mounting outrage over the death of Harambe, a 450-pound Western lowland silverback gorilla, aimed at both the zoo and the parents of the child.

The animal rights group Stop Animal Exploitation Now filed a negligence complaint against the zoo with the Department of Agriculture on Tuesday.

Meanwhile, an online petition at change.org has drawn more than 300,000 signatures demanding "Justice for Harambe", and calling for the parents of the child to be held accountable.

There was no indication from the authorities whether the proposed investigation would focus on the zoo or the child's parents.

Harambe was shot this weekend after he violently dragged and tossed the child who fell into his enclosure, officials said.

Michelle Gregg, the boy's mother, said on Facebook that people should not be "too quick" to judge and that "accidents happen", and also reported that her son had suffered a concussion and scrapes but was otherwise fine.

Her Facebook page has since been deleted.