"Concerning" emails continue to be received by schools, hospitals, courthouses, and places of worship across the nation on Friday.
Police acting assistant commissioner Naila Hassan said they believed the emails were coming from overseas.
While they had not yet been able to determine where the emails were coming from, Hassan said police were working with international partners to identify the source.
Hassan said the content of the emails would be distressing for those receiving them.
"They are bomb threats," she said.
"We won't go into any further specifics, what we can say is they will be quite distressing to those organisations that are receiving them."
Hassan said police were confident the threats were not credible.
"We do want to reiterate that this isn't targeted at any particular community or group, it is quite widespread.
"The digital environment is quite a complex environment, we can't always prevent these things happening but what we can do is we can assess threats of this nature and ensure that we keep our communities safe, and provide some reassurance and advice."
"We know that these emails are causing real concern among members of our community, particularly the emails directed at places of worship," an earlier statement said.
"Police remain confident that the emails being received are from the same source, and are not targeted at any particular community or group."
Another round of the same threatening emails received by hospitals and a school on Thursday were sent to more organisations this morning.
RNZ understands four hospitals and one school, Auckland's Saint Kentigern College, were searched by police or evacuated as a precaution yesterday.
A police spokesperson earlier confirmed the same email was sent to another round of organisations today.
Browns Bay School closed "until further notice due to receiving a bomb threat", it said in a message to parents.
Whangaparāoa Primary School also did, saying it too received a bomb threat.
"The emergency procedure is we need to clear everyone away from buildings and not allow people on site, until police clear our site," it said.
Auckland's Ōrewa College also sent a message to parents saying it was closing immediately due to health and safety.
RNZ understands the school may be a target of one of the emails.
The Education Ministry said the safety and well-being of school communities was its top priority.
Schools involved were doing an excellent job providing up-to-date information and assurance to their students, staff, and parent communities, the ministry said.
Police said they were confident the emails were being sent from the same source, and did not believe there was any actual threat to the places receiving them.
Any organisation that receives an email is asked to report it to police to help with the ongoing investigation to find its origin.
