Hunters say the Department of Conservation is coercing them into killing female tahr and their newborn kids.
Tahr are shaggy-haired brown goat-like game animals from the Himalayas, introduced to the Southern Alps a century ago for sporting shooters.
The department's Aoraki office has organised a cull of tahr in the Murchison Valley near Mount Cook until 24 December but has told hunters they will be given access only if they cull all tahr they encounter.
The Tahr Interest Group, which represents recreational hunters, says female tahr will begin giving birth in a couple of weeks.
Spokesperson Garry Ottmann says killing them during that time is cruel as their kids will be left to die of starvation.
"What we're saying is that is unacceptable, it is contrary to what we all believe in and it is contrary to the policies that we operate under."
Mr Ottman says the group is letting all hunters know they have no obligation to shoot female tahr.
But the Department of Conservation is defending the rules and says in a statement that it has already culled the tahr nannies and hunters will only be shooting males.
