Justice Minister Andrew Little and Google's New Zealand representatives met at Parliament last night where the head of the Google legal team in the United States joined the conversation on Skype.
Mr Little plans to follow up with the multinational company in the New Year to see what work, if any, they've done to fix their processes that led to the suppression breach.
Google's New Zealand government affairs manager Ross Young spoke to media after the meeting where he started by saying his heart went out to the family of Grace Millane.
The 26-year-old man charged with murdering her appeared in court on Monday last week and was granted interim name suppression.
Google didn't receive the court order until Friday and by then had already named the accused man in an email to anyone signed up to its "what's trending in New Zealand" service.
Asked why it took so long for the court order to make its way to Google, Mr Young said he didn't know.
He went on to say a process was in place for dealing with court orders that allowed Google to ensure they were acting appropriately and swiftly.
"Google respects New Zealand law and we understand what the concerns are in this very sensitive matter. But Google has acted on this situation, we have had a constructive discussion today ... explaining our processes and looking at how we can address similar situations in the future.''
Mr Young said there were trillions of web pages on the internet, which made it difficult to respond as quickly as some would like.
Mr Little asked to meet with Google to explain the importance of defending and protecting the integrity of the judicial system.
He described the meeting as constructive but was clear that if Google wanted to operate in New Zealand they would have to comply with the laws.
"Publishing across borders might be the reality of the world today but no justice system should be held to ransom and told that your orders to ensure a fair trial are no longer relevant.
"That's simply not acceptable anywhere," he said.
Mr Little accepted Google took the issue seriously and saw the gravity of it and would make sure they were not in breach of New Zealand's suppression orders again.