South Korea said it is considering tightening its social distancing rules as it reported 629 new coronavirus cases on Friday, the most since the first wave of infections in the country peaked in late February.

Prime Minister Chung Sye-kyun said the situation was critical as infections continued to rise at an alarming rate despite the reimposition of social distancing rules late last month.

The government would decide on Sunday whether to upgrade restrictions, he said.

"It's been 10 days since we upgraded the social distancing rules to phase 2 in the Seoul metropolitan area, but the transmission still seems to be uncontainable," Chung told a government meeting according to Yonhap news agency.

Of the new cases, 295 were from Seoul, the Korea Disease Control and Prevention Agency reported. South Korea has now reported a total of 36,332 infections, with 536 deaths.

Authorities are concerned that university entrance exams, which nearly half a million students took on Thursday, could prove to be another source of infections.

Chung urged students to refrain from visiting high-risk areas such as karaoke bars and internet cafes as they celebrate the end of the exam period.