Foreign Minister Winston Peters says the Red Cross' belief that it had the Government's support for the public release of Louise Akavi's name is "balderdash" and a "screw-up".
And he said he will release proof, if necessary, to show that the Government opposed the public release of her name, which he said further endangers Akavi's life.
Meanwhile Prime Minister Jacinda Ardern said she hopes the misunderstanding will not dampen the relationship or the ongoing efforts to search for missing nurse Louisa Akavi.
Yesterday Ardern said the Government objected to the decision by the International Committee of the Red Cross (ICRC) to release Akavi's name as part of a public plea for any information that could lead to her location.
Akavi, a 62-year-old nurse, was working for the Red Cross when she was taken hostage in Syria by the Islamic State five and half years ago.
Her captivity was kept quiet as part of an agreement between successive governments and media because of concerns she would be killed by her captors.
The last of Islamic State's territory was wiped out with the fall of Baghouz last month, but security forces have not yet been able to find Akavi or get confirmation of whether she is still alive.
ICRC director of operations Dominik Stillhart said yesterday he was surprised by Ardern's comments about not supporting the ICRC decision to go public.
"We would not have made that decision without the support of the New Zealand Government."
But this morning, in an interview with Sky News, Peters shot back.
"It's balderdash. It's not true. The reality is the media people we have worked with very closely ... all know we have been strenuous about keeping this secret in the interests of trying to preserve a chance to retrieve or save this woman, and that's still our view.
"We have not agreed with them. We made it very clear. We were doing it sometimes on a half-daily basis trying to convince them this was not a good strategy.
"If we have to release the proof of what we're saying, we will."
Peters said the Government will seek answers about how its communications were misinterpreted.
"We certainly will have them tell us why they screwed up this information, because a screw-up it is, and I'm sad about that, because the Red Cross in the main does a great job."
This morning Ardern told Newstalk ZB that the ICRC may have misunderstood the Government's acknowledgement of its decision as support.
"We were aware of their plans but did not see that as endorsement."
Ardern said she hoped the misunderstanding would not affect the ongoing search for Akavi.
"That shouldn't undermine the fact that over a number of years there has been co-ordination and collaboration between New Zealand and the Red Cross
"I wouldn't want to see that undermined by this different perspective."
That was also Stillhart's view, who said yesterday: "I have no reason to believe that what happened today ... is going to undermine or make this quest more difficult ... We have built a relationship of trust and confidence [with the Government] and I am absolutely sure that this will continue."
He said an attempt to rescue Akavi at the end of 2017 was very close to success.
"We believe strongly that she is actually alive ... We continue to look for her."
Stillhart said the ICRC had operational teams and networks in Syria and Iraq that were looking for Akavi, but would not go into details around what they were doing.
"Every decision, including this one, was to maximise the chances of winning Louisa's freedom."