Superintendent Chris Scahill said the calls might have been computer generated."We are very aware of very similar incidents occurring around the world, in particular the United States, UK and recently Australia," he said.
Bomb threats in those countries involved recorded voice messages being directed at schools.
"We're currently investigating whether we are the latest in this long string of incidents," Mr Scahill said.
If it was found that the calls were from overseas, the New Zealand police would be very limited in their ability to prosecute.
"The reality is tracking the calls can be challenging to bring this back to a particular location or person responsible," Mr Scahill said.
He said the threats were serious but were well managed by local police and school management.
Earlier, a police statement said officers were in attendance at each school and were "working with the leadership teams to determine the individual response at each".
"The priority for police and the schools is to ensure the safety of students and staff.
"Police have well-established procedures for dealing with such incidents..." In Tauranga, Brookfield School took all its pupils to a nearby reserve.
Principal Robert Hyndman said parents were advised to pick up their children and take them home if they could.
He said the police gave the school the all-clear at 2.35pm.
No bomb was found.
At Napier's Tamatea High, students and staff were also evacuated.
Principal Robin Fabish said a person called the school's reception and made the threat about 12.30pm.
"I don't know exactly what the caller said, or even their gender, but they said a bomb had been planted in the school," he said.
"We were unsure whether it was just a hoax or if it was real so we called police straight away and set the school alarm off so everyone would gather on the field."
Mr Fabish explained to the 350 students and staff on campus at the time that a bomb threat had been made, and everyone was sent home.
Police arrived shortly afterwards and began searching the school, he said.
Mr Fabish has been principal of Tamatea High for only 14 weeks.
"But I've been working at schools for a long time and it's the first time in my career something like this has happened.
"It's a bit scary when you're responsible for other people's kids."