(CNN) South Korea's capital Thursday began asking more than 1,500 people to self-quarantine -- and is considering measures to force their isolation -- because they unknowingly attended a symposium with a doctor who was infected with MERS, Seoul's mayor said.

The announcement by Mayor Park Won-soon came amid a MERS outbreak in South Korea, where the respiratory virus has killed four people since May and more than 1,000 schools have been shut to prevent the virus's spread.

A doctor -- one of 41 confirmed to have Middle East Respiratory Syndrome in South Korea -- attended the symposium in Seoul in late May, after he began to have symptoms, Park said.

The doctor, who had treated a MERS patient earlier in the month, was quarantined May 30 and tested positive for MERS on June 1, Park said.

MERS spreads from close contact with an ill person, such as living with or caring for them, according to the U.S. Centers for Disease Control and Prevention

But Park said all 1,565 people who attended the symposium should stay at home as a precaution, to avoid spreading the disease in the unlikely event that they contracted MERS at the meeting.

The mayor said the city is considering measures that would force these people to stay at home, and that officials are trying to determine where else the doctor traveled while he had symptoms.

It wasn't immediately clear how long the mayor wanted those who attended the symposium to stay at home. The CDC says the incubation period for MERS usually is five to six days, but can be as long as two weeks.

South Korea's Ministry of Health reported the fourth death.

A ministry spokesperson says the latest victim was a 76-year-old man who died Thursday. The patient, who had been suffering from asthma and chronic lung disease, was treated for three days last month at a hospital, where it's believed he contracted the virus.

The MERS outbreak in South Korea is the largest outside Saudi Arabia.

The first South Korean case, concerning a man who returned to the country after traveling to Saudi Arabia, Qatar, the UAE and Bahrain, was reported on May 20. The person had not been ill during his travels, according to the World Health Organization.

The extent of the outbreak has taken many by surprise -- mainly because the virus has not been shown to spread easily between humans and the health care system in the country is considered to be sophisticated and modern.

President Park Geun-hye acknowledged problems in the country's early response earlier this week.

"Initial reaction for new infectious diseases like MERS is very important, but there were some insufficiency in the initial response, including the judgment on its contagiousness," she said.

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The virus acts like a cold and attacks the respiratory system, the CDC has said. But symptoms, which include fever and a cough, are severe and can lead to pneumonia and kidney failure.

About three to four out of every 10 people reported with MERS have died. But those who died usually had underlying medical conditions that made them more vulnerable. In at least three cases, the patients had asthma and chronic pulmonary disease.

As of Wednesday, there have been 1,179 confirmed cases of MERS reported to WHO since 2012, and at least 442 cases were fatal. Cases have been reported in 25 countries , with China and South Korea joining the ranks only last month, WHO said.

MERS has been linked to camels and it's possible that some people became infected after coming into contact with camels, but it's not clear.

There are no vaccines and no cures.

To prevent MERS, the CDC recommends everyday hygiene practices like hand-washing, covering coughs and sneezes, and avoiding personal contact with sick people.