Asst Comm O'Brien said police would continue to support schools if the hoax calls continued.
“Police will work with the Ministry of Education to help make sure schools are prepared.”
From the information police had, the nature of the threats and the way they were coordinated, they believed the risk level was low, he said.
But he encouraged schools to be vigilant if they received a threat.
Asst Comm O'Brien said most of the phone call threats referred to an explosive device, which was why they believed the calls were coming from the same person.
Asked if the caller was demanding anything, such as money, he said he did not want to go into specifics. However, the calls were threatening harm to a degree that schools had no option but to take them seriously.
He was not 100 percent certain they were coming from offshore but said police were looking into that possibility.
They had not ruled out a domestic caller.
“It's really important for us to get to the bottom of where they are originating from, and obviously hold the person or persons accountable for these actions.
Asst Comm O'Brien said the incident was similar to the global so-called “robo-hoaxes” that happened in 2016-17.
Police worked with their international partners at the time and the perpetrator, who was based in Israel, was identified and held to account.
Meantime Education Minister Chris Hipkins has hit out at the threats, describing them as “very irresponsible”.
Asst Comm O'Brien told Radio New Zealand police would work with international partners to make sure the caller gets punished.
Anyone with information is encouraged to contact police.
Asst Comm O'Brien said they wanted to reassure students and parents that police were doing “everything possible to locate the source of the calls”.