Detective Sergeant Mark McCloy said police were still investigating who had fired the fatal shot, but were not considering members of the man's own hunting party.
"It was another hunting party that was involved," he said.
It was not known from what range Mr Hill had been shot. It was also unclear whether the shot hunter had been wearing high-visibility clothing.
Mr McCloy said the area was not heavily populated with hunters at the time of the incident.
Police would talk to other hunters in the area over the next couple of days.
"We're endeavouring to speak to other persons involved in the other hunting parties, and we'll be conducting a further scene examination in the coming days."
A post-mortem examination was due to take place in Invercargill this morning.
Police were alerted to the incident by a member of Mr Hill's hunting party, who walked out of the forest and notified Tuatapere police about 1.30pm.
A helicopter winched police and a medic from Te Anau into the heavily bushed area. Mr Hill's body was then recovered by helicopter.
The death comes amid "the roar" - the prime deer-hunting season between April and May, when stags come out in force to mark their territory.
Mr McCloy reminded hunters to be safe.
"All hunters are reminded that this is a busy time in the bush and it is imperative that you identify your target. If in doubt, do not fire."
