The blaze raced through the Sejong Hospital in the southeastern city of Miryang on Friday, killing 37 people, many of them elderly. The blaze began at the general ward's first-floor emergency room and most of the dead were from the first and second floors, the National Fire Agency official said.
The official says the cause of the fire was under investigation.
In the message, Francis said he was praying for the dead and that the wounded heal.
By yesterday afternoon, police had cordoned off the hospital as forensic investigators combed the smoke-blackened building.
Firefighters battling the blaze, which broke out at the rear of the emergency room on the hospital's first floor. Some carried patients on their backs to other rescuers below, who moved them on stretchers to ambulances. Those on upper floors used ladders and plastic escape slides to flee. It took emergency responders three hours before the fire was completely extinguished. But the officials later corrected this, saying some victims were counted twice.
It would be the country's deadliest fire in nearly 10 years, and the death toll is likely to increase with numerous injured in serious condition.
South Korea is one of the fastest-aging countries in the world and has many nursing hospitals, which are preferred for elderly people who need long-term doctors' care.
Super Blue Blood Moon incoming: Watch it when and where
The moon will be visible in large parts of USA , northeastern Europe, Russia, Asia, the Indian Ocean, the Pacific and Australia. If that crossing corresponds to a full moon, the moon will pass into the earth's shadow, resulting in a total lunar eclipse .
Dr Song said the six-storey hospital did not have a sprinkler system and was not large enough to require one under the law. The nursing home and hospital between them have about 200 beds.
If safety issues were involved in the fire, hospital and local authorities are likely to receive harsh public criticism.
Francis visited South Korea in August 2014. Officials blamed crew members' negligence, overloaded cargo, improper storage, unprofessional rescue work and corruption by the ship's owners.
South Korean President Moon Jae-in convened an emergency meeting and ordered a thorough response to the blaze.
At least 41 persons have been killed and dozens injured on Friday in a fire that engulfed a hospital in South Korea, media reports said.
Firefighters expect the number of casualties will rise further, according to South Korea's official news agency, Yonhap.
Kim reported from Seoul, South Korea.