Seven injured soldiers were taken to hospital, some in serious but stable conditions, and are receiving treatment for non-life-threatening injuries.
The Bushmaster vehicle rolled near Howard Springs RAAF base about 8.30pm on Wednesday.
NT Chief Minister Natasha Fyles said she been in touch with the East Timor ambassador in Canberra.
"It is early and our focus right now is on caring for those individuals, both Australian and Timorese Defence personnel," she said on Thursday.
"Their families should be reassured that we can provide such high-quality care."
The soldiers were training as part of Exercise Predator's Run 2023, the Northern Territory's largest annual military exercise.
It was the second serious accident since the exercise kicked off last week after three US marines were killed and 20 others injured when their aircraft plunged to the ground on a remote NT island on Sunday.
Ms Fyles would not be drawn on whether the training exercise should be cancelled after the horror first week.
"That would be a question for Defence, but what I can say is that we do need to make sure that our personnel have access to that training," she said.
"It does highlight the risk that our defence personnel undertakes not just in active service, but also in training."
The bodies of Captain Eleanor LeBeau, 29, Corporal Spencer Collart, 21, and Major Tobin Lewis, 37, were recovered from the crash site on Tuesday and remain in Darwin.
A ramp ceremony will be held later in the week to mark the start of the marines' journey back to the US.
An investigation is under way on the Tiwi Islands into what caused the fatal air crash.
