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 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."
Earlier this morning Peters said Stillhart's comments were "balderdash" because the Government had been clear from the beginning that it did not support the decision.
This afternoon Peters stood by his comments, but added that it was not helpful to continue to be asked about the misunderstanding.
"The message that was being carried was balderdash. That's a very polite way of describing how one person has, in my view, dropped the ball so to speak.
"I don't want to condemn a highly worthy international organisation. I don't want to get engaged in a dispute on it, and I don't want of our teams [looking for her] detoured by this conversation."
Peters said the Government could not have done anything more to stop the ICRC from going public, even though the Government, in partnership with international partners, may have known more about Akavi's possible whereabouts than the ICRC did.
The Ministry of Foreign Affairs has been sharing information with the ICRC, he added.
He echoed Stillhart's comments yesterday in saying that there have been times when rescue teams in Syria were very close to finding Akavi.
"We do think that on the way through there were occasions when we were highly encouraged by what was happening. And then something would happen and change and all of a sudden, we were further away from our target.
"It's sad. The fact of the matter is we went there looking for someone in the most extremely difficult, changing circumstances. And we've never given up hope and we're not giving up hope now.
"A humanitarian effort of her kind deserves a response from a country."
The terrorist attack in Christchurch and subsequent call from Islamic State for revenge was not a factor in the Government's decisions, Peters said.
He echoed Ardern's comments this morning about hoping the misunderstanding will not dampen the relationship with the ICRC, or the ongoing efforts to search for Akavi.
"I wouldn't want to see that undermined by this different perspective," Ardern told Newstalk ZB.
She said the ICRC may have misunderstood the Government's acknowledgement of its decision as support.
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."