Mr Gunner has also signalled the likely scrapping of check-ins at shops and other venues in upcoming reviews of virus restrictions.
"We are actively discussing moving on from the indoor mask mandates," he told ABC radio on Tuesday.
"I can't give you a date yet, but it will be sooner rather than later."
Mr Gunner said in relation to the check-in app, a two-step approach was more likely with the system to continue in a modified form to verify a person's vaccination status.
"It's a really simple measure for us to be able to do that," he said.
"I think there will become a point where we'll probably step past that as well.
Mr Gunner's comments came as health officials reported the death of a man in his 80s with COVID-19, taking the Territory's toll since the start of the pandemic to 16.
SecureNT said the man had underlying health conditions and died in Alice Springs Hospital.
Also on Tuesday, the Territory reported another 716 new virus infections.
There are currently 123 patients in hospital with the disease with three of those in intensive care.
Active cases across the Territory stand at 5754.
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