Breaching the name suppression of the man accused of Grace Millane's murder could result in the killer walking free, says the Justice Minister.

At least one overseas media outlet published the 26-year-old's name after his court appearance on Monday, and while the name was later removed from the online article it spread via social media.

Andrew Little says this is a serious breach of judicial law and could mean whoever killed the 22-year-old backpacker is never held to justice.

"It will not do justice to the Millane family if the accused in this case gets to walk away from facing justice because somebody else disclosed his details and he is able to say he won't get a fair trial," he told Newshub on Tuesday.

"That's why we have suppression rules. Like them or not, we have to abide by the ruling of the court."

He acknowledged that information can spread very quickly through social media, but wouldn't comment if he believes New Zealand's suppression laws are out of date.

"The internet might be one thing, fair trial rights are another, and if we want to make sure that the meticulous work of the police in putting together the case and proving it beyond reasonable doubt isn't in vain, then we want to make sure that people get fair trial rights.

"If that means a name is suppressed for whatever period of time then we've got to abide by that."

Mr Little said the accused's defence team "will be looking for every opportunity" to say their client's fair trial rights have been compromised.

"It's bad enough if an innocent person goes to jail. It's equally an injustice if a guilty person gets to walk free because the justice system has failed them."

Because New Zealand courts cannot enforce suppression internationally, Mr Little said it's up to us to make sure court rulings are abided by.

"The suppression orders handed down by the New Zealand court have to be adhered to in New Zealand. The guy at some point will face court and potentially a trial in New Zealand. We've got to do everything we can to make sure he gets fair trial rights.

"In the end if he doesn't, and he gets to walk away, that's a further injustice to the Millane family."

Police have issued a statement reminding the public that it is an offence to name someone who has been granted suppression, including writing the name on social media.

Deputy Prime Minister Winston Peters told RadioLIVE's Mark Sainsbury that Ms Millane's death is a sad time for all Kiwis.

"It's a very emotional moment when such a tragedy happens. Of course it happens to far too many families in our country, whether they're visitors or domestic."

He wouldn't comment when asked whether it was appropriate that the Prime Minister apologised to the Millane family on behalf of all New Zealanders during Monday's post-Cabinet press conference.

"I can't pass a judgment on that, it's just a sad time for our country."

Mr Peters said the murder, which has attracted international attention, will inevitably damage New Zealand's reputation as a safe place to visit.

"Of course it does, tourism is a very important thing, but the number one obligation of a government is the safety and security of its people. It's damaging to the New Zealand population as well."

Newshub.