TOKYO — South Korea scrambled Wednesday to try to contain an outbreak of Middle East respiratory syndrome, a virus that has already claimed two lives in the country, with more than 1,300 people quarantined and upwards of 500 schools set to close their doors Thursday.

Amid criticism it has been too slow to respond to the virus, which has no vaccine or cure, President Park Geun-hye ordered the establishment of a task force to try to contain the infection and to be more transparent along the way.

“There are a lot people worried about this situation,” Park told an emergency meeting of officials and health experts Wednesday. “We must make the utmost effort to stop MERS from spreading.”

The case brings back memories of severe acute respiratory syndrome, or SARS, that began in Asia in 2003, spreading to Europe and the Americas and leading to 774 deaths worldwide, according to the Centers for Disease Control. Fearful that MERS has already spread, China is also taking measures to contain it.

Two people have died from MERS in South Korea, while 28 others have been confirmed as having the virus, five of them on Wednesday alone. This makes the outbreak the largest outside Saudi Arabia, where MERS began three years ago, the World Health Organization said, warning that “further cases can be expected.”

Another 398 cases are suspected and a total of 1,364 more people have been quarantined, the vast majority of them at home.

Education authorities have left it to principals to decide whether to shut their schools, and 200 kindergartens and schools closed their doors on Wednesday while more than 500 planned to shut on Thursday. Almost all of them are in Gyeonggi province, the area around Seoul, where the first patient with the virus sought treatment, although six elementary schools and a middle school in Seoul will also close until Friday at parents’ request.

Drugstores reported a run on surgical masks and hand sanitizer as fear about a wider outbreak spread.

MERS arrived in South Korea in a 68-year-old “index patient” who had traveled to four countries in the Middle East and showed no symptoms when he returned home on May 4.

But a week later, he sought treatment at two outpatient clinics and then two hospitals, potentially exposing a large number of health-care workers and other patients to the virus.

“Given the number of clinics and hospitals that cared for the index case, further cases can be expected,” the World Health Organization said in a statement.

The two patients who died, a 58-year-old woman and a 71-year-old man, had both been in contact with the index patient in the hospital and both had other health problems that could have weakened their ability to fight the infection. The exposure times could have been as short as five minutes to a few hours, the WHO said.

The South Korean government has come under fire for refusing to disclose the names of the clinics and hospitals where the index patient sought treatment. But three doctors at the emergency meeting Wednesday rejected demands for greater openness, Yonhap News Agency reported, saying that 25 out of 30 people were infected at a single hospital, which has since closed to new patients.

Meanwhile, Chinese authorities quarantined 88 people, including 14 South Koreans, after a 44-year-old South Korean man, the son of one of the people who has contracted the virus, defied medical advice and flew to Hong Kong on May 26 while he had symptoms of the virus. He then traveled to the southern Chinese province of Guangdong by bus.

China informed WHO on May 29 that the man had tested positive for the virus and had been isolated at a hospital in Huizhou, Guangdong, while Chinese authorities try to track down other people who might have been exposed.