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The blaze occurred at the Sejong Hospital in Miryang city. It started around 7.30 am in an emergency room of the hospital, Xinhua news agency reported.
Firefighters took about one hour and 40 minutes to put out the blaze, which started when there were approximately 200 people in the building, Yonhap news agency quoted an official as saying.
According to Yonhap, 93 patients from the nursing home were safely evacuated. Fire chief Choi Man-woo told reporters that the cause of the fire was not yet known.
Pictures from the scene showed the building engulfed by heavy grey smoke as well as patients being rescued. It is South Korea's deadliest fire in almost a decade and the toll is expected to rise, the BBC said.
Several of the injured were reported to be critical.
Most patients at the hospital were either of cerebrovascular disease or stroke. Most victims died from smoke inhalation, reports said.
South Korean President Moon Jae-in convened an emergency meeting and ordered a thorough response to the blaze.
Miryang is about 270 km south-east of the capital here. The hospital has been operating since 2008. The nursing home and hospital between them have about 200 beds.
About 35 medical staff work at the hospital, according to the government official.
Friday's blaze comes just a month after 29 people were killed in Jecheon in a blaze at a public gym.
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Some of the survivors were still recovering at hospitals while others were already in their homes