Detective Inspector Bridget Doell, of the Northland criminal investigation branch, said police “are aware of some activity on social media, which we are making further inquiries into”.
“I acknowledge the public’s feeling about this tragic case,” Doell said.
“However, I must remind the public that it is an offence to breach a court order, and this includes naming someone who has name suppression on social media.”
She said anyone who saw a post that breached the suppression order shouldn’t share the post.
It is an offence to publish anything which could identify a person whose name was suppressed by law under the Criminal Procedure Act 2011.
The maximum penalty for breaching a suppression order is six months’ jail or a $25,000 fine.
Police were called to a Ruakākā property, south of Whangarei, around 6.25am last Monday, where officers discovered the children’s bodies.
A family friend of the Ruakākā whānau described seeing the “lovely kids” the day before they died.