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SEOUL, South Korea — At meetings of the secretive Shincheonji Church of Jesus, worshipers sit packed together on the floor, wearing no glasses — or face masks. They come to church even when sick, former members say. After services, they split up into groups for Bible study, or to go out into the streets and proselytize.

After the first coronavirus infection was reported among its members, they were told to lie about being followers, though the church later said that was not its policy.

Now, health officials are zeroing in on the church’s practices as they seek to contain South Korea’s alarming coronavirus outbreak, in which members of Shincheonji, along with their relatives and others who got the virus from them, account for more than half of the confirmed infections. On Saturday, the number of cases in the country soared to 346 — second only to mainland China, if the outbreak on the Diamond Princess cruise ship is excluded from Japan’s count.

More than 1,250 other church members have reported potential symptoms, health officials said, raising the possibility that the nation’s caseload could soon skyrocket further. In response, the government is shutting down thousands of day-care facilities, nursing homes and community centers, even banning the outdoor political rallies that are a feature of life in downtown Seoul.