Government restrictions on where helicopters can fly make it difficult for hunters to find other places to hunt tahr, according to Tahr Foundation chairman Snow Hewetson.
In a statement yesterday, New Zealand Conservation Authority chairman Edward Ellison supported the Department of Conservation's plan to eradicate tahr from the Aoraki/Mt Cook and Westland Tai Poutini National Parks.
Ellison also said the two parks made up "roughly 20 per cent" of the tahr feral range.
"So there is significant alternate opportunity for tahr hunting in New Zealand to continue on public conservation land."
Hewetson described that suggestion as "a bit disingenuous".
Much of the feral range for tahr beyond the national parks was covered by no-fly zones and classified as wilderness areas, he said.
Some areas could not be accessed at all, and others were balloted to hunters for six-week periods in winter.
"There's a whole lot of country we cannot access.
"You can't fly in and it's physically impossible to walk into a lot of it."
Hewetson said the access issue had been raised as far back as the 1993 Himalayan tahr control plan.
"I've even had an email from one of the members of the Conservation Authority saying they support hunters' calls for better access.
"But nothing's ever been done about that."
Mr Ellison said the number of tahr had increased to at least three to four times the 10,000 maximum agreed in the 1993 control plan.
Last year, the authority urged the Government to remove all tahr from the parks and it was "pleased to see that this initiative is now being included in Doc's operational plan".
Professional Hunting Guides Association president James Cagney said yesterday tahr hunting provided hundreds of jobs and a "multimillion-dollar benefit" to the country.
Members were "shocked" by the Doc plan, he said.
"It would effectively decimate the tahr population in the Southern Alps and, if successful, will throw hundreds of people out of work."