SEOUL - South Korea is grappling with a growing number of elderly coronavirus patients as well as a rise in untraceable cases.

The authorities are worried as infections stemming from Seoul-based health product retailer Richway, whose target market is the elderly, are spreading.

This is even as they warned that the rise in untraceable cases could complicate efforts to curb the spread of the virus.

Of the 618 cases detected in the first two weeks of June, mostly in Seoul and the surrounding Gyeonggi province, 10.2 per cent had unknown transmission routes, said the Korea Centres for Disease Control and Prevention (KCDC).

This marked the first time that the figure hit double digits. It is also double the 5 per cent mark that the health authorities had hoped to maintain under, in order to effectively manage the outbreak. Anything higher could trigger a wider chain of infections, they said.

To make things worse, about half of all infections are asymptomatic, making them hard to detect.

"As we don't know who is infected or not, it's important for everyone to follow hygiene rules (as recommended by the government) in their everyday life and practise social distancing," KCDC director Jung Eun-kyeong said at a press briefing on Monday (June 15).

Once the second-most infected country after China, where the virus was first reported, South Korea has managed to flatten the infection curve with massive testing, aggressive contact tracing, and strict social distancing.

However, there are now fears of a second wave due to the emergence of cluster outbreaks. The number of daily cases hovers around 30 to 50.

The country on Monday reported 37 new cases, bringing the total to 12,121. The death toll stood at 277.

Health Minister Park Neung-hoo said there have been 27 cluster outbreaks since early May, when the government eased social distancing rules citing a drop in the daily number of cases to below 50, and the number of untraceable cases below 5 per cent.

He added that the situation in the capital area is serious, as infections from Richway have spread to at least eight other places. Richway is a door-to-door sales company that organises marketing events targeting elderly people, such as health seminars and recreational activities, so as to sell products to them.

The number of cases traced back to the cluster has grown to 169, including 41 who had personally visited the company.

A 72-year-old man working for Richway first tested positive on June 2, prompting the authorities to test his 10 co-workers and 188 people who visited the office in Seoul's Gwanak district from May 22 to June 1.

Infections have since spread to an interior design company (32 cases), a separate door-to-door sales company (16), an English private academy (14), a call centre (11), a shelter for Chinese migrants (eight) and three churches (25).

An employee of Myeongseong Housing, the interior design company, tested positive on June 7, after visiting Richway on May 30. The virus was then transmitted by another Myeongseong worker to the English private academy she attends, leading to 14 infections there. Another student then spread the virus to at least two other people who went to the same gym as he did.

Health officials are particularly concerned about the Richway cluster as it infected many senior citizens - the most vulnerable group with the highest fatality rate. Data shows that 40 per cent of new cases confirmed from June 7-13 were in their 60s or older.

The KCDC has since urged the elderly to stop gathering in small, cramped rooms without windows. If they do, they must avoid eating and singing, and must wear a face mask and use hand sanitiser.

"Old people tend to have weaker immune systems, which means the consequences of infection can be fatal," Mr Park said.

To contain the recent outbreaks, which also include a cluster linked to Seoul's clubbing district Itaewon and e-commerce giant Coupang's distribution facility in Bucheon city, strict social distancing measures in Seoul, Gyeonggi and Incheon city have been extended "indefinitely" as of last Friday.

This means that public facilities such as museums and libraries would remain closed, and will not reopen until the number of daily cases go down to single digits. Entertainment facilities such as bars and clubs will also remain shut, while companies are advised to allow flexible work arrangements.