South Korea said on Tuesday it will open school classes online next week and reschedule its annual college entrance exams slated for November as concerns persist over the coronavirus and small outbreaks continue to emerge.

The country has postponed the beginning of all schools' new semester three times from early March to April 6 amid a rise in confirmed virus patients.

After a big early outbreak, South Korea has largely managed to bring down its daily number of new cases to around 100 or less, but infections from small clusters including churches, hospitals and nursing homes, as well as imported cases, continue to arise.

Prime Minister Chung Sye-kyun said the country is not ready yet to open schools as before despite the government's efforts to prevent the spread of the virus.

"We regret that we have not reached levels where children can go to schools safely even though we mobilised all our capabilities to substantially decrease risks of infection," Chung told a meeting of government officials, according to his office.

"It is difficult to guarantee the safety of children as the sizable number of new patients emerge every day, and there are concerns that it might spread again from schools to homes and communities."

Schools will provide online classes starting April 9, Chung said, vowing to ensure students' access to technology at home to minimise any study gap. The highly competitive annual college entrance exam, held every October, will need to be postponed.

The Korea Centers for Disease Control and Prevention reported 125 new coronavirus cases on Tuesday, bringing the total infections to 9,786. The death toll stood at 162.

The daily tally has been hovering slightly above 100 or less for the past three weeks, but the latest number marked an uptick from 78 recorded on Monday.

Of the new cases, 60 were from the hard-hit southeastern city of Daegu, where a hospital saw more than 75 infections over the past few days, KCDC data showed.