The prime minister has directly raised the government's concerns about the treatment of name suppression with Google executives in Davos.
Jacinda Ardern has been in Switzerland for the World Economic Forum, with an invite to the dinner as part of her trip.
The issue of breach of name suppression online blew up last year, when Google users were sent an email naming the man accused of killing British tourist Grace Millane in defiance of a court suppression order.
The 26-year-old man charged with her murder appeared in court and was granted interim name suppression.
But Google said it had not received the order until days later. Asked why it took so long for the court order to reach them, Google's New Zealand government affairs manager Ross 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.''
At the time, Google reassured the public that it would take measures to ensure such a breach did not happen again.
"There are some controls in place to ensure the alert doesn't feature inappropriate content (for example adult content) and the trending query needs to have an associated news story," the company said in a statement.
One statement also said the email in question reached "less than a few hundred people".
Ms Ardern has used the opportunity in Davos to raise it again.
A spokesperson for the prime minister said she was given an assurance by Google executives they would look into it further, and will come back to the government in the near future.
Justice Minister Andrew Little also demanded a please explain at a Beehive meeting last December.