A conservation plan is being developed to protect the Ben Ohau Ranges in the Southern Alps from Himalayan tahr.
The Department of Conservation (DoC) said tahr were wrecking native alpine tussocks in their search for food and destroying the ecosystems.
It hoped that a renewed focus on tahr would help reduce the population.
Tahr control programme manager James Holborow said the only way to kill them was by shooting, either from a helicopter or on the ground.
"So high numbers of tahr have quite strong localised impacts, we won't necessarily see those impacts everywhere in the environment. But what we see is tahr tend to herd together and where they herd together, they'll tend to have quite strong effects."