More than 70 are said to be injured.
According to the Yonhap news agency, eight of those injured are in critical condition.
Earlier it was reported that 31 people have been killed and more than 40 others were critically injured in the incident.
The blaze is suspected to have started in the emergency room on the first floor of the main building of Sejong Hospital in the city.
A dozen firefighters arrived at the scene and managed to douse out the blaze in just under two hours.
The fire authorities had said that they have transferred around 38 people, mostly patients to four nearby hospitals.
Around 93 more patients from the nursing home adjoining the hospital building escaped when the fire broke out and are safe.
Approximately 100 patients were believed to have been inside the hospital building when the fire broke out. (ANI)