Two-year-old Joe Massa went into cardiac arrest and died in September after he and his parents waited more than two hours in the emergency department at Sydney's Northern Beaches Hospital.
The hospital, opened in 2018, is operated by private provider Healthscope, which is owned by Canadian private equity giant Brookfield under a controversial public-private partnership set up by the previous coalition government.
Under the model, Healthscope has a contract with the NSW government to run the hospital's public wing until 2038.
NSW Health Minister Ryan Park said he would push for improvements in care at the hospital in light of the toddler's death, adding that he did not believe the public-private model was the best for healthcare.
"I've got to now try and make sure that this hospital is as strong and as robust and as reliable, and most importantly as safe as possible," he told Sydney radio 2GB on Friday.
"What we need to do at the moment, while Healthscope are still operating this facility, is making sure that they are doing so in a safe, effective way that meets the needs of the community."
In the case of Joe "we have not only failed to meet the needs of the community, we've catastrophically let down a family", Mr Park said.
Joe's parents Elouise and Danny Massa said staff and management at the hospital failed their son after he presented with hypovolemia, a condition that occurs when the body loses too much fluid.
The couple claimed staff ignored critical warning signs such as the toddler's high heart rate, which went up to 192 beats per minute within 30 minutes.
The boy also exhibited signs of limpness and a rash, and he lost consciousness, the parents said.
"He had his whole life ahead of him and we trusted Northern Beaches Hospital to provide the care he needed," they said in a statement.
Healthscope, which has reviewed the toddler's interaction with the hospital, apologised for the death and pledged to improve systems, including on triage.
Federal Opposition Leader Peter Dutton said the circumstances were "unimaginable" for the family, adding that they deserved answers about what happened to their son.
The incident comes as the controversial facility on Friday dodged planned industrial action by the NSW nurses union over claims of under-staffing levels at Healthscope-run hospitals.
The company runs 38 hospitals nationwide, including the $600 million 488-bed  Northern Beaches Hospital which has previously suffered from medical supply shortages, staffing issues and patient wait times exceeding 24 hours.
NSW Nurses and Midwives Association Assistant General Secretary Michael Whaites said the union would press for extra staff at Healthscope facilities, despite the Fair Work Commission suspending the planned industrial action late on Thursday.
"We know that the staffing levels across many Healthscope facilities are below that of the public sector," he said.
