Justice Minister Andrew Little has met with Google executives after the internet giant published the name of the man accused of killing Grace Millane.
Little said they had a "constructive discussion".
He said Google has indicated to see what they can do with their systems to prevent another suppression breach like this occurring again.
Google representative Ross Young said they understand New Zealand law and has acted on the situation.
"Google does receive court orders, including suppression orders," he said.
Young said they received the Millane court order on Friday, December 14, following the court appearance on Monday.
Little said in the end he has to defend the integrity of New Zealand's justice systems and the meeting with Google addressed this.
Google said they would look at their systems in order to ensure another breach would not take place again.
The Minister will meet with Google in the new year to discuss how they are getting on resolving the issue.
Little said New Zealand media were unethical to name the Australian Catholic priest currently under trial following Google's breach.
At the end of the day, Little said if Google want to operate in New Zealand they have to comply with our laws.
Google under fire
Google has been under fire for the past two weeks after it emailed the accused man's name to Kiwi internet users.
An email was sent to anyone signed up to its "what's trending in New Zealand" service, despite the man being granted name suppression by a district court judge.
Since sending the email Google has defended itself, claiming it was unaware of the name suppression.
Millane was last seen alive on December 1, the day before her 22nd birthday.
Her body was eventually found in bush on the side of Scenic Drive in the Waitākere Ranges a week later.
A 26-year-old man has been charged with her murder.
Little had already rebuked UK media for naming the accused and said Google stepped over the line as well.
He said Google's excuse wasn't good enough and he was not prepared to accept that they simply weren't aware of the suppression order.
"This thing about they didn't know it was suppressed, I simply don't accept that," Little said.
"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."
More than 100,000 searches of the 26-year-old's name were also made following his court appearance last week, according to the email Google sent out.
The Silicon Valley company's publicly available analytics also showed the accused's name was the second-most searched item in New Zealand with over 50,000 searches.
A Google spokesperson told the Herald it would comply with any court order it was made aware of, however, they said initial investigations by the company showed it did not know about the suppression order.
"We respect New Zealand law and understand the concerns around what is clearly a sensitive case," the spokesperson said.
"When we receive valid court orders, including suppression orders, we review and respond appropriately. In this case, we didn't receive an order to take action. We are looking for ways to better ensure courts have the tools to quickly and easily provide these orders to us in the future."
The spokesperson said its Google trends alerts are automatically generated by its algorithms and are based on searches over a time period in a selected geography.