Justice Minister Andrew Little is meeting Google representatives on Tuesday to make it clear that the integrity of fair trial rights cannot be left to "algorithms and machines".

This week search giant Google appeared to break the name suppression order of the man accused of murdering British woman Grace Millane by emailing the man's name to anyone signed up to its "what's trending in New Zealand" email.

The accused had applied for name suppression in Auckland District Court on Monday, and appealed when it was refused - invoking an automatic 20-working-day suppression order.

Little said he was meeting with New Zealand representatives from Google, but there may also be representatives from Google's California and London offices, which showed Google was "taking it very seriously".

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"They hoover up news, produced by legitimate news outlets, and distribute it around the world on the basis of algorithms and their machinery without caring about whether or not that information is the subject of suppression orders, and whether or not it potentially compromises justice.

"They need to understand that that's the risk they're taking. So I'll explain that."

A Google spokesperson has said the tech giant would comply with any court order, but it didn't know about the suppression order in the Millane case.

Little said that excuse wasn't good enough.

"This thing about they didn't know it was suppressed, I simply don't accept that.

"Irrespective of that, and yes, this might be the way of the world and modern technology, but the reality is that we cannot surrender the effective administration of justice to algorithms and machines and say, 'Well, that's it, it's all over for fair trial rights.'

"We cannot allow that to happen."

Little said if fair trial rights were compromised, "nobody gets justice".

"It's not just the defendant directly affected. It's the victim as well. We have these rules for the benefit of victims as much as anybody."

Earlier this week, Little chastised British media for naming the accused, and now a close friend of the Millane family has written to London's major newspapers asking them to refrain from breaking name suppression.

The Government has said it is not currently looking at changing the laws around name suppression, even though the 20-working day suppression order has been criticised as too long.

Little said that New Zealand media also should respect suppression in other countries, given that some New Zealand media had named a public figure who has name suppression and faces historical sex charges in Australia.

"We should be respecting suppression orders handed down by other judicial systems to make sure fair trial rights are not compromised on those countries," Little said.

"To the extent that New Zealand media have not honoured that, I think that is grossly unfair."