Authorities revised the death toll down from 39 on Friday afternoon, but a Miryang City official warned it could rise as at least 18 patients remained in critical condition.
The fire comes less than a month after a similar tragedy left 29 dead in the city of Jecheon
, raising concerns over lax safety standards in the country.
Officials said they were still investigating the cause of Friday's fire, which is believed to have started around 7:20 a.m. local time in the emergency room on the first floor of the 98-bed Sejong Hospital.
Rescue services took three hours to completely extinguish the flames, which engulfed the first two floors of the six-story building in Miryang, which is about 270 kilometers (168 miles) southeast of the capital, Seoul.
Sprinklers were not installed in the building due to its small size, the hospital's chairman, Son Kyung-chul, told reporters.
Patients had breathing problems, difficulty walking
The hospital's director bowed in apology to the patients and victim's families during the briefing. Seok Gyeong-sik also said he would do his best to take care of the incident.
The majority of those killed in the blaze are believed to be elderly patients, said Chun Jae-kyung, head of the public medical center in Miryang.
"Because the hospital had many intensive care units and elderly patients, there were a lot of people with breathing problems," Chun said. Most of the deaths were due to smoke inhalation.
The hospital is adjacent to a nursing home and shares many of the same facilities. All the patients inside the nursing home were rescued, authorities confirmed.
Footage aired on local TV showed emergency workers battling the blaze, as hospital staff rushed to evacuate patients, carrying those unable to walk on their backs.
Kim Dae-hyun, the owner of a shop next to the hospital, told CNN that many of the patients at the dual medical facility were in their 80s and 90s and were unable to walk without help.
By late afternoon Friday, emergency personnel had posed a list of names identifying the victims onto a wall close to the hospital. Patients' family members crowded to check the pages.
Fire safety rules questioned
For many in South Korea, Friday's blaze will bring back painful memories of 2014, when a fire at a nursing home in the southern county of Jangseong killed 21 patients
, many of whom were left trapped due to their inability to escape unaided.
The recent spate of deadly fires in South Korea has led to questions over the government's ability to enforce sufficient safety measures.
Two men were arrested following the deadly building fire in December that killed 29 people. The building's owner is accused of violating fire safety regulations and committing involuntary homicide by negligence. The building's manager is accused of involuntary homicide.
That fire is suspected to have started in a parked vehicle on the ground floor and quickly consumed the eight-story building. Many of the bodies were found in a public bath on the second floor.
After Friday's fire, South Korean President Moon Jae-in called an emergency staff meeting. In a statement, Moon promised to quickly identify the cause of the fire in order "to prevent the recurrence of the fire in the future."