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The family of the toddler who fell into an exhibit at the Cincinnati Zoo said those who wish to send them money should instead donate to the zoo in honor of Harambe, the beloved gorilla shot dead in order to protect the boy.

"Some have offered money to the family, which we do not want and will not accept," the family said in a statement. "If anyone wishes to make a gift, we recommend a donation to the Cincinnati Zoo in Harambe’s name.”

The family added that the boy "had a checkup by his doctor and is still doing well."

The Cincinnati Zoo in a statement said "If you are interested in supporting gorilla conservation in honor of Harambe, you can donate to the Mbeli Bai Study," which operates in the Republic of Congo.

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The child slipped through the barrier of the gorilla's enclosure Saturday and tumbled more than 10 feet, coming face-to-face with 17-year-old Harambe, a 450-pound western lowland gorilla. For 10 terrifying minutes, Harambe alternated between gently pawing him and dragging him through a moat.

Related: Killed Gorilla Seem to Protect Child Who Fell in Enclosure: Witness

Zoo authorities tried to coax the critically endangered gorilla away from the child. When they were unable to do so, they made the decision to fatally shoot the animal.

The family's statement came a day after Hamilton County prosecutor Joseph Deters announced that Cincinnati police are investigating whether any criminal charges should be filed in the incident.

Harambe, a 17-year-old male gorilla, was shot dead Saturday after a child fell into his enclosure. Cincinnati Zoo

The zoo's decision has prompted outrage from the public, many of whom have called for negligence charges to be filed against the family.

Thane Maynard, the zoo director, has said the facility stands by its choice to shoot rather than tranquilize Harambe, which may have taken too long to take effect before the boy could be rescued.

"We'd make the same decision today," Maynard said Monday.

Related: Harambe, Gorilla Killed at Cincinnati Zoo, 'Had to Pay the Price': Experts

Ed Hansen, CEO of the American Association of Zoo Keepers, told NBC News a tranquilizer dart could have taken up to 30 minutes to work, leaving the zoo no choice but to kill the gorilla.

"The tranquilizer possibly could have worked, but the key term there is 'possibly.' And if you were to fire a dart at an animal, he could react violently to the first opportunity that presents itself, and that would have been that small child," Hansen said Tuesday. "Unfortunately for the gorilla, the only really positive way to ensure the safety of the child was to dispatch the lethal force."

Maynard said he had received an outpouring of responses from colleagues around the world, including famed primatologist Jane Goodall.

On Tuesday, the Jane Goodall Institute published the email Goodall had sent, which read in part: "Dear Thane, I feel so sorry for you, having to try to defend something which you may well disapprove of ... it is a devastating loss to the zoo, and to the gorillas."

The Brownsville, Texas, Gladys Porter Zoo, where Harambe was born and raised before he transferred to Cincinnati for its breeding program, set up a conservation fund in Harambe's memory. It wasn't immediately clear if the Cincinnati Zoo had a fund set up.