A scared father said one 12-year-old girl, who was a sibling of a high school student, had received a message saying, "I'm going to come to your house and rape you", with her home address then sent to her phone.
Police Inspector Callum McNeil said today's complaint related to a threatening message sent to a student from Westlake Girls High School.
"We are also aware of other third-party information that students from Albany Senior High School have received similar messages on Instagram," McNeil said.
Police were now working with Albany Senior High School as well.
"However, what would be most beneficial is for anyone who has received these messages to contact Police directly via their local station or by contacting 105 quoting file number 210617/9027," he said.
He said police were investigating the messages "but still need to hear from anyone who can help us to identify the person or persons responsible for sending these messages".
Some males had been wrongly accused of sending the messages and so police asked the community to please leave it for police to investigate.
"We are treating it seriously and with urgency," NcNeil said.
The father who spoke to the Herald described the threats as "really violent and terrifying".
He understood thousands of messages had been sent to students attending his daughter's North Shore school.
He didn't want to be named out of fear his daughter could be identified and receive further abuse.
His daughter was sent a message - seen by the Herald - saying: "I'm going to send a butcher's knife through your skull."
The father described his daughter as a "resilient wee character" who had been providing support to other affected students.
The threatening messages were being sent from an anonymous account. It's understood the account was being used by multiple people because they were popping up at different areas quite quickly on Snapchat maps, the father said.
"So they'll pop up in Takapuna and then two minutes later, they'll be out at Whangaparāoa and then back at Albany, so it's jumping all over the place.
"There have been some examples where they specifically talk about a guy's girlfriend and say what they are going to do to the girlfriend."
The cyber abuse escalated when the fake social media account was posted online claiming the culprit was a male ASHS student, principal Claire Amos told the Herald.
However, that student had been wrongly accused, said Amos - who is also on the board of independent online safety organisation Netsafe.
The father said one of the students was threatening to hurt the boy, and was aghast that an innocent child could have ended up badly injured on school grounds.
Amos said she first became aware of the cyber abuse affecting Albany Senior High students after receiving emails from anonymous Gmail addresses last week.
She sent an email to all parents last night alerting them to the threats.
"Last week, on Thursday, we became aware of a situation where social media accounts (Instagram and SnapChat) were created under a male name.
"Both social media accounts became very active very quickly, making inappropriate and offensive remarks about young women," the email said.
"We have reported any accounts we are aware of. Netsafe and the Police are actively involved in this case and we encourage you to pass on any information that you have to Netsafe and the Police as it may further support their investigation.
"We understand these incidents can be very distressing, and we are doing our best to ensure our young people are being supported."
The principal told the Herald the school had also been doing work to educate students about online safety and the harm of spreading potential misinformation.
"It's been a really upsetting and complex situation."
Meanwhile, NetSafe chief executive Martin Cocker told the Herald there had been a spike in the past month of social media abuse towards young people and "a handful" of schools across the country had been affected.
"The truth is we are seeing an escalation of this around the country," Coker said.
"We are seeing accusations of sexual assault being published and we are also seeing threats of [sexual assault], and in quite significantly higher numbers than we would normally so it's definitely something that's happening now and is of some concern."