Grace Millane: PM Jacinda Ardern won't support Millane's alleged killer being granted secrecy

Prime Minister Jacinda Ardern says people can probably read between the lines about her thoughts on the alleged murderer of British backpacker Grace Millane getting name suppression.

The identity of the 26-year-old man charged with murdering Ms Millane was supressed for an interim period on Monday but quickly spread on social media after being printed in several British tabloids.

While Ms Ardern wouldn't say if the man deserved to have his identity kept private, she said people could probably understand how she felt.

"Ultimately in this case, I think probably people would anticipate the kinds of things that I would say, so it's best that I leave it to the courts," she said.

It followed the Prime Minister choking up on Monday as she delivered a heart-felt apology to the family of Ms Millane.

"I cannot imagine the grief of her family and what they would be experiencing and feeling right now, she said at her post-Cabinet press conference.

"On behalf of New Zealand, I want to apologise to Grace's family."

Ms Ardern told The AM Show the name suppression law is one of many different pieces of legislation which were affected by social media.

"There is no doubt the environment has changed. Name suppression in a modern age is a different thing than it was 20 years ago," she said.

She also said there were issues with clean slate laws which allowed individuals with non-custodial sentences to have their crimes "essentially sealed" after a certain amount of time.

As those crimes and the history of individuals can be easily searched online, such legislation can be difficult to apply.

Ms Ardern said New Zealanders felt a sense of shame about Ms Millane's death due to the responsibility Kiwis feel for anyone who travels to Aotearoa.

"When we encounter a tourist, we are very keen to know how they are enjoying themselves, what their favourite sites are. We are very mindful of our responsibility to individuals who visit here and I think that carries over to their safety," she said.

Ms Millane was visiting New Zealand during a year-long OE. She was reported missing last Wednesday and on Sunday police found a body in the Waitākere Ranges which is believed to be that of Ms Millane.