The soldier is accused of being a member of two far-right groups, and possessing a copy of the March 15 terror attacks, according to charging documents previously obtained by RNZ.
He has been on military arrest and was due to appear today for the second pre-trial court-martial in a case that has garnered media attention globally.
The soldier, who has interim name suppression, was arrested in December 2019 after a joint investigation by police and the Defence Force.
He was due to appear before Chief Judge Kevin Riordan at Linton Military Camp today, however the 28-year-old's attendance was excused for a number of reasons including issues surrounding his mental health.
The hearing was to determine what evidence needed to be disclosed to his defence lawyers ahead of the trial.
It related to the New Zealand Security Intelligence Service and the information proposed for disclosure was highly classified.
The hearing was adjourned to manage that classified information but reporters, attending virtually, were asked to leave first.
By law, reporters can be asked to leave a court if security levels exceed a certain threshold, namely when discussions are centred around national security.
No new date has been set down in the case which was delayed from last year.