The email was released to the Herald in a mostly-redacted tranche of Mfat material under the Official Information Act.
The OIA documents show several emails indicating a flurry of activity in the week leading up the Akavi's name becoming public on April 15.
That activity involved New Zealand's UN representative in Geneva Jillian Dempster, New Zealand ambassador to the Netherlands and Denmark Lyndal Walker, and ICRC representatives.
Prior to her appointment as ambassador, Walker led Mfat's response to major international incidents affecting New Zealand citizens.
The ICRC sent a draft of the media statement to Mfat on April 12.
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.
Islamic State territory was wiped out with the fall of Baghouz in March this year, but security forces have not yet been able to find Akavi or get confirmation of whether she is still alive.
The ICRC decided to name her in a public statement on April 15 as part of a public plea for any information that could lead to her location.
ICRC director of operations Dominik Stillhart said the decision had the support of the New Zealand Government, but Prime Minister Jacinda Ardern said it was her preference to continue the search without publicly releasing her name.
"It absolutely remains the Government's view that it would be preferable if this case were not in the public domain," Ardern said at the time, standing by the long-held position that doing so could endanger her life.
Ardern said at the time that her position was made clear to the ICRC, but Stillhart, speaking from Geneva, was surprised by Ardern's comments, adding that going public would not have happened without the New Zealand Government's support.
A spokesman for Ardern said at the time that it was possible the Government's acknowledgement of the ICRC's intentions could have been misinterpreted as support, but Stillhart's comments were inaccurate and "somewhat frustrating".
The apparent disagreement between Stillhart and Ardern was noted in an Mfat sitrep report just after the story broke, and an Mfat representative in Geneva met with the ICRC that night.
The sitrep report also noted that the story was widely covered in Arabic language media, which focused on the deployment of elite New Zealand SAS troops in Iraq looking for Akavi.
"There has been no coverage thus far on Iraqi media of Louisa ... The websites and social media of the Iraqi Prime Minister's office and Unami (United Nations Assistance Mission for Iraq) have not referred to the case."
The sitrep report said that the story was covered in Syria, Egypt, Kuwait and Jordan.
Stillhart said in April that he did not think the apparent misunderstanding would affect the search for Akavi.
The Red Cross said the release of her name in April led to a lot of information coming forward, but would not reveal the nature of that information.
The search for Akavi is continuing.
