The number of infections rose to 64 after 14 new cases, including one death, of Middle East Respiratory Syndrome (MERS) were confirmed last night, the health ministry said.
All of the 14 were among group of 1,820 quarantined after being exposed to those diagnosed earlier, it added.
However, Busan city authorities reported an additional case in the country's southern port and second-largest city, sparking alarm that the outbreak may spread nationwide.
The case was not included among the 14 new infections confirmed by the health ministry.
Also Read
He urged the public not to panic, saying all 64 patients had already been in hospital.
"We can put the situation under control because... The outbreak is not spreading to the outside community," Choi said in a press conference.
"People should not overreact and should cooperate closely (with the government) to minimise negative impact on the economy," he said.
The government will step up monitoring on those placed under observation, including tracking the locations of those in quarantine at home via their mobile phones, Choi said.
The administration of President Park Geun-Hye and health officials have come under a storm of criticism over perceived slow and insufficient response to the outbreak.
A policy not to name the hospitals where patients were diagnosed or treated was a major focus of public criticism.
Choi on Sunday disclosed the list of 24 such hospitals -- mostly in Seoul or Gyeongi province surrounding the capital -- saying it was aimed at "easing public anxiety."
Bigger budget support was also promised for those placed under quarantine and for local governments and school authorities struggling to contain the outbreak.
The first case -- reported on May 20 -- was of a 68-year-old man diagnosed in the city of Pyeongtaek, about 65 kilometers south of Seoul, after a trip to Saudi Arabia.