Justice Minister Andrew Little says global giant Google is "flipping the bird" at New Zealand laws by breaking suppression orders in the Grace Millane murder case and then doing nothing about it.

"Google's contempt for New Zealand law, and for Grace Millane's family is unacceptable, and I will now be considering my options," Little said.

Lowndes Jordan partner Rick Shera says those options should include going legal.

"Sabre rattling and wringing of hands by the Minister and, previously, the Privacy Commissioner, is good, but court proceedings should be issued if laws have been broken and Google or any other provider is unwilling to accept responsibility," Shera posted.

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In follow-up comments to the Herald, the tech law specialist noted a bill going through Parliament would create a $100,000 fine for corporates who break a suppression order (an individual can be fined up to $25,000 or receive a prison sentence up to six months).

"That is clearly de minimis [chump change] for the likes of Google or Facebook," Shera said.

"The bigger issue for them is being found to have broken the law - the reputational effect - and the precedent effect overseas."

Departing NZRise co-chair Don Christie offered the blunter comment that, "Seems simple to me. They should charge Ross Young. He's the Google rep in NZ."

Young is Google's government affairs manager in NZ.

In December, Little chewed out Google for by emailing the Grace Millane murder-accused's name to anyone signed up to its "what's trending in New Zealand" email.

Google executives also gave Prime Minister Jacinda Ardern assurances that the matter would be looked at when they met in Europe in January, and Ministry of Justice officials followed up with Google in March and again this week.

But yesterday Little said Google had contacted him - via an email from Young - to say that there was no plan to change anything.

In an earlier High Court at Auckland hearing, on the case of a white collar worker who was trying to get his name removed from search results relating to a controversial incident, Google used two arguments that could resurface in any legal action around the Grace Millane incident.

One was that it argued it was a neutral platform rather than a publisher. The other was that the case should be pursued through courts in the US - home to Google NZ's corporate parent and its technology services.

That case petered out.

Shera says an attempt to take Google to court over name suppression would also be fraught.

"Any court proceeding is messy. Don't let anyone tell you otherwise," he said.

"The issue is one of jurisdiction really and it's hard to predict how a court would go - but someone has to hold their feet to the fire."