Hawke's Bay's top cop says those questioning why police shot a man at Flaxmere Primary School should look to the United States and its history of mass school shootings.

Eastern District Commander Tania Kura told RNZ's Morning Report she understands questions will be raised by the general public around Tuesday's incident.

Kura said the man had links to both a staff member and student at the school.

He had visited the school twice before on Tuesday, before police were called out to reports of him having a firearm about 2.11pm, she said.

The fact a man was in the school's courtyard, with what police had been told was a firearm, meant the public should "look to the States to see what tragic circumstances can happen there", Kura said.

"I feel like (police) go out every day and have to make quick decisions and in a dynamic situation you gotta factor in schools finishing, parents are arriving, somebody could have walked into that court yard.

"There's a lot of things you have to factor in and make that split-second decision," she said.

A man, in his 30s, who was shot once, was on Wednesday morning in a stable condition under police guard at Hawke's Bay Hospital.

"There'd been something brewing for him but we don't know what he was thinking at that particular time," Kura said.

Police inquiries were continuing.

"The people who were involved - the staff and the family members - are actually quite in shock and we're just giving them some time to gather their thoughts while we're speaking to them."

The man may have been armed, police cannot yet confirm if he was, but was not threatening staff or children, Kura said.

He indicated he wanted to speak to a specific staff member and it was hard to detail what was happening in his head, and if the staff or children were in any danger, Kura said.

Investigations by the IPCA are also under way.

"It will be gone over with a fine-tooth comb," Kura said.

"It's a big deal to actually shoot someone and the staff are often quite traumatised by that as well, so we put welfare and support systems in and around them."