The child stabbed in the head in a classroom altercation in Mangere hasn't woken from his coma since the incident.
The 11-year-old victim was believed to have been stabbed with scissors during a fight at the Pacific Christian School with another boy about midday on Tuesday.
Since emergency surgery that day, the boy has been in a coma at the Starship children's hospital.
His family are gathered at his bedside. He remains in a critical condition, and it is not known whether he will pull through.
If he does not survive, police will then have to decide whether to charge his 11-year-old alleged attacker.
"It will be very much a case of the next few days to see what happens," Detective Inspector Dave Lynch said.
Due to the age of the alleged offender, police say no charges can be laid in relation to the fight.
The only charges a minor under the age of 12 can face are murder and manslaughter.
Police were still interviewing about a dozen children who witnessed the attack in the Mangere classroom.
The children were unsupervised at the time; the teacher was out of the room, Mr Lynch said.
A source close to the family of the alleged attacker this week said he had been "really, really badly" bullied for more than a year - allegations they claim were not investigated by the Pacific Christian School.
The school would not comment this week on whether bullying was an issue and did not return calls yesterday.
Labour education spokesman Chris Hipkins said he would have "expected" the school to investigate any bullying allegations, with Ministry of Education assistance.
"A serious matter like that raised by the family, the ministry should look very closely - with the school - to get to the bottom of things.
"In any case, where there's allegations of bullying, the school needs to thoroughly investigate it."
Ministry of Education head of sector enablement and support Katrina Casey said advice and support would be offered to the school.
There was nothing the ministry could force the private school to do.
"Schools are responsible for managing behaviour - including bullying - in collaboration with parents and the wider community. We provide a range of support for schools to help them do this. In a state school, we would support the board of trustees in any investigation into bullying, where that was requested.
"Even though Pacific Christian School is a private school, we are happy to similarly support its principal or board of proprietors in any investigation into bullying, if they receive a complaint."
In some cases, schools would be advised to involve other agencies, such as the police or Child, Youth and Family, she said.
The ministry would be offering the school support in implementing the practices from a new anti-bully book, released last week.
"We will continue to work with the school for as long as needed and are happy to support it with any issues."