'Don't be evil' NZ tells Google

New Zealand's justice minister has urged Alphabet's Google not to be "evil" after the company failed to abide by a suppression order related to the murder case of a British backpacker.

The killing of 22-year-old Grace Millane last year shocked New Zealand, where serious crimes are relatively rare and its cities and countryside are considered safe.

A New Zealand man accused of the crime pleaded not guilty in January and his name has been suppressed by a court in Auckland.

However, the man's name appeared in Google's "what's trending in New Zealand" email that was sent to thousands of subscribers.

Despite assurances from Google in meetings with government officials, the issue remains unresolved, said Justice Minister Andrew Little.

"My message to Google is, don't be evil. Do the right thing," Little said in a video posted on his Twitter account, referring to the company's former motto "don't be evil".

"We've had a situation where, in a very important trial - the Grace Millane case - a newspaper, helped by Google, has published information that the judge said was suppressed," Little said.

"That's wrong and I've been a bit frustrated by Google not working out what the problem is and what they can do to prevent this from happening again," he added.

A Google representative said the company respects New Zealand law and understands the sensitivity around this issue.

"When we receive valid court orders, including suppression orders, we review and respond appropriately," the representative said in an emailed statement to Reuters.

Millane, who was travelling after finishing university, went missing in Auckland, New Zealand's largest city, on December 1.

Police found her body in a bush area just a few metres from a scenic drive in Auckland's Waitakere Ranges.

Prime Minister Jacinda Ardern is leading a global campaign to stop social media like Facebook, Google and others from being used to promote terrorism and violent extremism after a mass shooting in Christchurch in March.

Ardern said she was disappointed by Google's response in the Millane case.

"Now we need to consider what the next steps will be for NZ," Ardern told reporters on Wednesday.