"There may still be more fatalities, I hope not, but that possibility exists," police inspector Roberto Ramos told the media on Friday, Efe news reported.
Some people were still trying to determine the whereabouts of loved ones among the 103 patients inside Badim Hospital when the blaze erupted Thursday evening.
The Rio coroner's office said that some of the victims died of smoke inhalation, while others perished as a result of the failure of respirators and other life-support devices.
Four firefighters were injured battling the fire, which the hospital blamed on a short circuit in a generator.
Hospital staff scrambled to evacuate the patients and set up a makeshift infirmary on the street.
All but 13 of the patients were ultimately transferred to eight other medical facilities in Rio.
Mayor Marcelo Crivella told media at the hospital on Friday morning that the building was outfitted with all legally required fire-safety equipment.
The police and fire departments have already begun an investigation to confirm the cause of the blaze.
"We're still carrying out a study to learn where the fire began," Ramos said. "We know that the generator burned, but what we're seeking is to know the spark that started it."
Rio de Janeiro's Civil Defence department said Friday morning on Twitter that it had been working at the scene since the previous evening along with a group of eight technicians.
It added that that team had cordoned off Badim Hospital and its surrounding area and was currently awaiting clearance from police to inspect the building's structure.
The department said residents of about six properties located near the hospital had been instructed to evacuate their homes as a precaution.