The South endured one of the worst early outbreaks of the disease outside China but appears to have brought it broadly under control thanks to an extensive "trace, test and treat" program while never imposing a compulsory lockdown.

Social distancing rules were relaxed after a public holiday in early May and the country has since been returning largely to normal.

But in the last month the South has seen around 35 to 50 cases a day, mostly in the Seoul metropolitan area where half of the population lives.

"We believe the second wave has been running since it was triggered by the May holiday," said Jung Eun-kyeong, director of Korea's Centers for Disease Control and Prevention.

Officials reimposed some social distancing measures in late May following fresh clusters in and near Seoul, and most cases reported in the past week have been domestic infections.

Of the 46 new cases reported Tuesday -- taking the country's total to 12,484 -- 30 were people arriving from overseas.

Seoul Mayor Park Won-soon warned on Monday that the capital would have to go back to strict social distancing measures if the number of infections in the city topped 30 on each of the next three days. On Tuesday, six were announced.

If the capital failed to tackle the current trend in transmission, the daily case count could reach "about 800" in a month's time, he said.

South Korean President Moon Jae-in said Tuesday he is "confident" the virus "still can be controlled".

"What has been discovered in the past five months is that you can prevent virus infections as long as you follow the basic disinfection rules and the government's guidelines," he said.