At her weekly post-Cabinet media conference, Ms Ardern repeatedly refused to answer any questions about the fate of the Red Cross nurse who was kidnapped in 2013.
"You'll forgive me, I hope, for not commenting on that case. It remains the government's view that it would be preferable if the case was not in the public domain,'' she said.
"For that reason I won't be commenting further on it, with one exception, and that is to make special mention of the domestic media. I think the decisions that have been made over a period of time by various outlets and journalists has not only been responsible, I think it's been exemplary.
"I'm sure I speak on behalf of successive governments when I say thank you."
While the prime minister accepted there was "interest" in the case since it went public this morning, she said outside of the information already provided by the foreign affairs minister, there would be nothing further from the government.
"Decisions have been taken that were not our own and I won't be commenting any further on decisions made by others,'' she said.
Asked what the government's position on paying ransoms was, Ms Ardern said her view was that it "has not changed''.
"I'm not at this current point in time willing to be drawn individually on that policy but it's remained unchanged," she said.
Any messages to the family of Ms Akavi would be done privately, Ms Ardern said.
The International Committee of the Red Cross said it was surprised by the Prime Minister's objection to its decision to name Ms Akavi.
Director of Operations Dominik Stillhart said the Red Cross would not have made the decision without the support of the New Zealand government.
He said he was confident the decision had been made with full transparency and in coordination with the government.