Five more cases were confirmed on June 3 taking to 30 the number infected in the RoK since the outbreak began there two weeks ago. Two people have died, fuelling fear in the country with the most cases outside the Middle East, where the disease first appeared.
While there has been no sustained human-to-human transmission, the nightmare scenario is the virus changes and spreads rapidly, as Severe Acute Respiratory Syndrome (SARS) did in 2002-2003, killing about 800 people around the world.
MERS was first identified in humans in 2012 and is caused by a coronavirus from the same family as the one that triggered SARS. But MERS has a much higher death rate at 38%, according to World Health Organization (WHO) figures.
The WHO puts the total number of MERS cases globally at 1,161, with at least 436 related deaths, the vast majority in the Middle East. There is no cure or vaccine.
"There are a lot people worried about the situation," Park told an emergency meeting of ministers and top officials. "Everything must be done to stop any further spread."
More than 200 schools were shut on June 3, most of them in the province of Gyeonggi, around Seoul, where the first death occurred on June 1.
The Republic of Korea has quarantined or isolated about 1,300 people for possible MERS infection.
Media in the region has reported tourists cancelling visits to the RoK.