The overhaul to the SAS is one of nine changes the Defence Minister has promised to adopt after years of official inquiries.
The proposed changes were announced in Wellington today, where Henare also indicated a new Inspector-General could provide independent oversight of the NZDF.
Operation Burnham was a 2010 raid in Afghanistan's Tirgiran Valley. Authors Nicky Hager and Jon Stephenson in their 2017 book Hit & Run claimed the raid killed six civilians.
In April 2018 the Government announced an inquiry into Operation Burnham and related matters. Defence Force head Air Marshall Kevin Short later apologised for providing inaccurate information to the public about the operation which had led to five deaths, including a child.
Several of the recommendations announced today relate to organisation and information management.
But the Expert Review Group report explicitly suggested integrating one or more Special Operations staff officer roles into broader functions.
"I have huge respect for the SAS and their leadership and the way that they work across agencies," Henare told the Herald.
"What we're looking to do is strengthen that," he added.
"The special in SAS is really important," Provost said. "They are special. They are an elite force. They have very important capabilities that we need for the future and we saw nothing but things to admire.
"What we're looking at is marginal improvements, not making them like everybody else."
Provost said the NZDF had made several positive changes in recent years but there was room for improvement in strategic and corporate areas.
She said at present, the ministry's role was limited to the early stages of deployment.
Provost said work was needed to refresh the NZDF operating model and public affairs strategy.
She said there was no sense in civilians dictating military tactics but there did need to be more civilian input into broader strategy.
Provost said levels of trust in the SAS relied on how well the Defence Force leadership kept ministers, MPs and the public informed of special forces activities.
She also said the NZDF faced significant challenges with information and knowledge management.
"In some cases protecting information is literally a matter of life and death for NZ Defence Force personnel," Provost said today.
The changes will be rolled out from next year to 2025.
As the Herald reported in 2019, former Defence Force chief Tim Keating told an inquiry the military missed chances to earlier admit civilians may have been killed in the raid.
A file proving the NZDF had wrongly denied the possibility of civilian deaths ended up locked away in a safe for years.
Alexander Gillespie, University of Waikato Professor of Law, last year said the scandal was a humiliation for the NZDF and he predicted the force would be stripped of autonomy.