Justice Minister Andrew Little expects New Zealanders who shared the name of Grace Millane's killer via social media will face legal action.
At the weekend police reminded the public that it is an offence to breach a court order, such as name suppression, including naming someone on social media.
The situation has arisen because the name of the man convicted on Friday of killing UK backpacker Grace Millane remains suppressed by the courts.
Mr Little told Morning Report that while work is underway to set up an international mutual agreement on suppression breaches with countries like the UK, Canada and Australia, the law is very straightforward in New Zealand.
"If somebody in New Zealand goes on social media and publishes details that are suppressed, that's a matter of contempt of court in New Zealand. We've already got the power to deal with that and I understand authorities will be looking at situations where that has happened in the last couple of days."
Anyone who breaks the law in New Zealand could face a fine of up to $25,000 or six months in jail.
Mr Little said he will be meeting with law ministers from the Australian states this week to discuss his plan for international enforcement of suppression orders.
The United States and Commonwealth law ministers have also accepted that international agreements on suppression orders is worthwhile and the Commonwealth Secretariat has begun work on the proposal, although that may take up to two years, Mr Little said.
"Everywhere I've gone it's been well received - this idea about mutual recognition of suppression orders from other countries."
Grace Millane. Photo / Instagram
No plans to extend bill regarding sexual history evidence
Mr Little is not considering changes to the kinds of evidence juries can hear about a murder victim's sexual history in the wake of the Grace Millane trial.
A bill before Parliament will tighten the rules around evidence about a complainant's sexual history, to better protect against unnecessary and distressing questioning, for survivors of rape or sexual assault.
The legislation, aimed at making it easier for sexual violence victims to testify in court, has passed its first reading.
It proposes that unless a judge gives permission, a witness cannot be asked about their sexual history with the defendant, nor could they be asked about their sexual preferences.
Since a guilty verdict was returned for the man accused of killing Ms Millane, there have been calls for more protection of the sexual history of those who are killed in the course of a crime.
Mr Little told Morning Report there are no plans to broaden the bill.
"We have drafted the bill with the particular objectives in mind that we have which relates to trials related to sexual offending both in the criminal and civil jurisdiction. There is no intention to extend it beyond that."
He said he was limited in what he could say about the Grace Millane trial because the convicted man may appeal.
"...The other party potentially gets away with saying all sorts of things about the person who has died and it's never very clear where the truth lies ...
"But defence counsel have a job to put a case and to challenge assumptions and to challenge Crown evidence and they do that. I make no judgement at all about what happened in the Grace Millane trial."
He said he did not want to be drawn into defence tactics for a trial and sensitive evidence was often the subject of pre-trial decisions by the judge.
The aim of the current bill was to make the legal process less traumatising for victims when they gave evidence.
