Police and Victim Support staff continue to assist the families involved along with school staff and pupils.
The boy's distraught family said they are dealing with the tragedy "hour by hour".
The boy, who the Herald on Sunday has agreed not to name, is in an induced coma at Dunedin Hospital after surgery for a serious head injury.
His maternal grandfather said the family were "just coping".
"We are completely focused on my grandson," the man said yesterday. His Mum and Dad are coping but it is an hour-by-hour situation," he said.
The grandfather said the family had been trying to contact extended family to inform them what they were facing.
Police and emergency services were called to what has been described as "a tragic incident" at Sacred Heart School in Invercargill at 8.35am on Friday morning.
The boy was found with serious head injuries on school grounds. He was taken to Invercargill Hospital then transferred to Dunedin Hospital that afternoon.
The grandfather said police had asked the boy's family and the school not to discuss details of what happened.
"I've been instructed by the police not to say anything more than what has been said," the grandfather said. "They are just kids, it's just kids being kids. I haven't got all the details."
He said the brain surgery on Friday night "went as well as it could have" and his grandson was "stable but critical. We have to get through the next 24 hours," he said.
Sacred Heart School board of trustees chair Paul Brooks said the incident had rocked the school and the Ministry of Education was providing support to teachers, parents and pupils.
A team of at least 12 police officers were still conducting interviews with those present at the school that morning.
School principal Peter Forde said the incident was upsetting and the school's thoughts were with the family.
Forde and the Board of Trustees are meeting with Ministry of Education officials today to ensure the school is ready to open tomorrow.
- Herald on Sunday with NZME
