Justice Minister Andrew Little is putting multinational companies on notice over their obligations to follow suppression laws in New Zealand.
Mr Little has met with Google over an email alert it sent out naming the man accused of killing British tourist Grace Millane.
The 26-year-old's name is currently suppressed by the courts.
Google representatives have told Mr Little that they will look at what happened.
A follow-up meeting has been arranged for the new year.
Mr Little said it is about protecting and defending the judicial system for both those on trial and the victims.
"I accept they [Google] take the issue seriously, I accept that they see the gravity of it and I accept their assurance that they will now go away and look at their systems to make sure that they're not in breach of suppression orders in New Zealand again."
Ahead of the meeting, Mr Little said these big outfits like Google and Facebook have operations in New Zealand, and therefore they could be held responsible here even if the motivating force sits somewhere else.
"If we can't get through on a localised basis, then the next best thing is to look internationally, work with other countries," he said.
"In the last week, Australia has been afflicted with this problem in a very serious case.
"So I think there's a growing community of interest internationally that are keen to say 'you know what, we've got to preserve the integrity of our justice systems, and countries should reach agreement on how we can do that."
He said the answer could be as simple as agreeing to abide by the suppression laws of other countries, if they agree to follow ours.
"You don't need every single country to agree, but ideally you'd want as many as possible.
"But what you do need to do is send a signal to these big operations that there is cross border agreement and frankly we're coming after them."