Chief of Air Force, Air Vice Marshal Graham Lintott said Flight Sergeant Forster was a well-liked and respected flight sergeant, and his death had come "as a tremendous shock".
"Our focus now turns to Flight Sergeant Forster's family, his squadron colleagues, and many friends throughout the Defence Force and elsewhere. Our people have been with the family since [Thursday] morning and we will continue to support them in any way we can."
Prime Minister John Key expressed his sympathy for the two men.
"The brave men and women of the New Zealand military are constantly threatening their lives as they go about their duties and it's a tragic case when a New Zealander is lost in the service of his country and that's the situation today."
Defence force units continued training as usual yesterday, but those affected by the incident had been granted temporary leave.
Squadron Leader Kavae Tamariki said the death had rattled personnel at the training camp, the largest in the country. "There is a bit of shock and sadness at the loss of one of our own."
Defence Minister Wayne Mapp said: "There will be a full inquiry but he was essentially marking munitions for later disposal, which is an inherently dangerous task.
"It was an unexploded artillery round ... my understanding is that he was killed instantly."
Police and the Defence Force are involved in the inquiry.
It is the first serious accident during training at the Waiouru base since a live artillery round exploded inside a gun barrel in March 1997, killing two visiting Singaporean servicemen.
Twelve other servicemen were also injured in the explosion, including a staff sergeant from the New Zealand Defence Force.
An inquiry found that a defective fuse had caused a premature explosion.