A teacher has fatally stabbed an eight-year-old girl at an elementary school in South Korea, in an incident that has shocked the nation.

The female teacher, who is in her 40s, confessed to stabbing the student in the central city of Daejeon, police said.

The girl was found with stab wounds on the second floor of a school building at 18:00 local time (09:00 GMT) Monday and was pronounced dead at the hospital. The teacher was beside her with stab wounds that police said might be self-inflicted.

South Korea's acting president Choi Sang-mok on Tuesday ordered an investigation into the case and urged authorities to "implement necessary measures to ensure such incidents never happen again".

Some locals laid flowers and a stuffed doll at the gate of the school, which was closed on Tuesday.

The teacher had requested a six-month leave of absence citing depression on 9 December but she returned to school just 20 days later after a doctor assessed her as being fit to work, the Daejeon education office said.

She did not have a relationship with the student, authorities said.

Days before the stabbing, the teacher had displayed violent behaviour, including putting another teacher in a headlock, they said.

Two officials from the education office visited the school on Monday, the morning of the stabbing, to investigate that altercation.

The student was reported missing on Monday evening after the bus driver informed the school that she had not arrived to be picked up that day.

Police also said they would continue interrogating the teacher after she recovers from her surgery.

After the attack on the co-worker, the education office recommended that the teacher be put on leave and be separated physically from the other teacher.

She was made to sit beside the vice principal's desk so that she could be kept under close watch.

She had also not been teaching any classes since her leave in December, and did not have any contact with the eight-year-old student, the official said.

South Korea is a generally safe country with strict gun crontrol laws. But in recent years, it has grappled with several high-profile crimes, including stabbings.

"It pains me to see such incident because a school should be our safest space," said acting president Choi. "I offer my deep condolences to the victim's family who suffered great shock and agony."