Mr Harvey said police were nearing the end of their investigation into the incident.
"There's just some inquiries we're doing today and hopefully by the end of the day we should just about be finished.
"What I'd describe it as is an incident that occurred when two boys have been playing as boys do."
Police were yet to speak to the hospitalised 10-year-old, but were in contact with his family.
"He's slowly improving. He's out of the coma. He's actually talking to his parents and his family and they are looking at moving him into the children's ward, out of ICU," Mr Harvey said.
"We're just thankful that he's recovering, but he's still got a way to go."
A Ministry of Education specialist trauma team was at Sacred Heart School today, which was open as normal.
Board of trustees chairman Paul Brooks said the team included counsellors, although he was unable to say how long it would be there for.
The school was helping police with their inquiries.
"We are very pleased to hear that he's showing signs of recovery," Mr Brooks said of the injured boy.
The boy's grandfather has previously said the 10-year-old had brain surgery on Friday, which "went as well as it could have".
Ministry head of sector enablement and support Katrina Casey said the trauma team's role was to help the school return to its normal routines.
"The team talk to staff, the principal and board members. They brief staff on how students may respond to this difficult event and how to get access to additional specialist psychological support if it's needed for any individual students or staff members. "That support is there for as long as a school needs it."
Ms Casey said teams were drawn from staff at the ministry's regional offices.
"The nature of help offered varies depending on what the incident is, and how the school is affected," she said.
"If the school requests it, we can also provide extra resources to support the school. This could include relief staff who work alongside teachers or take on duties that will free up school staff to support and respond to the needs of the children."