South Korean coronavirus cases have doubled to 433 and there are fears the tally could surge again after more than 1000 people who went to a church at the centre of the outbreak reported flu-like symptoms.

South Korea's Centres for Disease Control and Prevention (KCDC) reported 142 new cases at a Saturday morning briefing and another 87 in the afternoon.

KCDC also reported another death from the virus, bringing the total to three.

Of the new cases, most have been linked to outbreaks at a branch of the Shincheonji Church of Jesus in the southeast city of Daegu and a hospital in Cheongdo county.

Samsung Electronics said one of the virus cases had been confirmed at its mobile device factory complex in Gumi, causing a shutdown of the facility there until Monday morning. Gumi is close to Daegu.

Samsung's factory in Gumi accounts for a small portion of its total smartphone production.

The government designated both Daegu, which has a population of 2.5 million people, and Cheongdo county, home to around 43,000 people, as "special care zones" on Friday.

Officials sent military medical staff and other health workers, and extra resources, including hospital beds.

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More than half of the national cases are linked to a 61-year-old woman known as "Patient 31" who attended religious services at a branch of the Shincheonji Church of Jesus in Daegu.

The woman had no recent record of overseas travel, authorities said.

KCDC said on Saturday they had obtained a list of 9300 people who had attended church services, around 1200 of whom had complained of flu-like symptoms.

The church and Cheongdo hospital outbreaks may also be linked, as several church members attended a funeral at the hospital for the brother of the church's founder this month.

President Moon Jae-in has called for officials to investigate potential links.

Cases from the hospital surged near a hundred overnight, with all but two of the new infections coming from the hospital's psychiatric unit, where KCDC director Jeong Eun-kyeong said patients often share rooms.

"We think the patients had repeated exposure given the isolated facility of the psychiatric wards, where many patients share the same room," she told reporters.

The hospital, which has around 600 patients and staff, has been closed and patients are being transferred to other facilities.

In the capital Seoul, thousands of people took to the streets on Saturday for regular weekend political rallies, despite the city's mayor on Friday saying the gatherings would be banned as part of containment measures.

North Gyeongsang Province governor Lee Cheol-woo said among the new confirmed cases were nine of the 39 South Koreans who went on a pilgrimage to Israel earlier this month.

The coronavirus originated in China before spreading to some 26 countries and territories outside mainland China.

The death toll from the outbreak in mainland China rose to 2345 as of Friday with over 76,000 people infected.