A number might appear to be from New Zealand but actually originate from overseas, police said.
"Until police can rule out any actual threat, we must take all these calls seriously and respond accordingly," police said in a statement.
"The safety of students, teachers and schools are our priority. We understand the fear and concern that this will cause, however we reiterate that so far we have not established any actual threat to any school."
Police are pursuing several lines of inquiry.
Police would not disclose the names of each school as the investigation was ongoing.
Police responded to today's bomb threats just before 12pm, when many schools were preparing to break for lunch.
Two Northland schools received the threats.
Kerikeri High School was evacuated as a precaution after receiving a threat. The Northern Advocate also understands a school in Kaitaia also received a threat.
Western Heights High School in Rotorua was placed in lockdown today due to threats.
A reporter at the school said no one was allowed in or out of the school, and students were taken to assembly points on the school grounds.
More than eight Auckland schools also reportedly received bomb threats today.
Glendowie Primary School Board of Trustees chairwoman Dawn Garbett said the school received a bomb threat from a caller about 12pm today.
Police told the school it was one of more than eight Auckland schools which had received threats.
"They said they were a bit stretched because all the calls came in around the same time," Ms Garbett said.
"We evacuated the buildings and called police. Police spent about half an hour doing a full sweep of the school but didn't find anything.
"We sent a note to parents and now the kids are out on the field having a great time, until their parents are able to come and pick them up."
Glen Eden Intermediate School, north of Titirangi, Auckland, also sent a note out to parents saying it had received a bomb threat today.
The note said the school office received a pre-recorded automated bomb threat just before 12pm.
The school was evacuated and students and staff assembled at Kaurilands Domain.
Police inspected the school and allowed students and staff to return just after 1pm.
Classes returned to normal this afternoon.
Yesterday, police said calls of a "concerning nature" were made to Logan Park High School in Dunedin, Wellington High School in Wellington, Burnside High School in Christchurch, Central Normal School in Palmerston North, Brookfield School in Tauranga and Tamatea High School in Napier.
- Additional reporting: Northern Advocate and Rotorua Daily Post
