Officials at the children's elementary school in Kawasaki City held a news conference on Tuesday evening.
The stabbings killed one girl and wounded 16 other students at the school.
Tetsuro Saito is head of Caritas Gakuen, which operates Caritas Elementary School.
He said he doesn't know how to express his anger over this attack on innocent children and the parents who love them. Saito said he shares the pain of the affected families.
Caritas Elementary School vice principal Satoru Shitori said he was helping children get on buses at a bus stop when he heard screams from the end of students' line.
He said he found a man holding what appeared to be kitchen knives in both hands, stabbing students without speaking and then running toward the bus station.
Shitori said the man stopped his attacks on the children when he ran after him. He said a bus driver got off a bus and began pursuing him.
The vice principal said he reported the incident to police, called for ambulances and then contacted the school.
He said he checked students' injuries and other damage while calling the police. He said he instructed about 20 uninjured children to board their buses.
Shitori said he then went to check on students who were lying on the ground.
He said he also found five injured students and about 15 other children taking shelter at a nearby convenience store.
Before the news conference, the school briefed parents on the stabbings. About 1,000 parents of all Caritas schools attended the hour-long session.
The participants said the school explained how they should deal with their children's mental health.
A father who attended the briefing said he no longer knows how adults can protect children.
He said he hopes for a society where children can go to school without fear.
The father said he cannot bear to think how the parents of the dead girl must be feeling. He added that he has no thoughts about the perpetrator at the moment.