A petition to halt the cull of tens of thousands of South Island Tahr has attracted more than 20,000 signatures in just 15 hours.
But Conservation Minister, and Green Party MP, Eugenie Sage has called the National Party-organised petition "absurd".
Last week, Sage instructed the Department of Conservation (DOC) to cull 17,500 of the goat-like animals this weekend.
The Tahr population on public conservation land has climbed to an estimated 35,600 –which is 26,000 more than that what is allowed, under the Himalayan Tahr control plan.
DOC and recreational and commercial hunting groups have together been removing an average of about 4600 Tahr each year.
"This hasn't been enough to keep the population under control and we need to be doing more," said DOC Eastern South Island Operations Director Andy Roberts.
Sage said the animals are an invasive species that eat their way through precious native plants, damaging the indigenous vegetation.
The estimated Tahr population figure came from aerial counts which have been independently analysed by DOC across the past 18 months, she said.
But the Tahr foundation has questioned DoC's figures, saying they have been "hastily gathered".
National's Conservation Spokeswoman Sarah Dowie agrees, saying the cull will be based on "anecdotal evidence [done] without a proper consultation process with recreational hunters".
Although she agrees the Tahr population needs to be responsibly managed, she said DOC needed to have better consultation with on-the-ground hunters.
And more than 20,000 Kiwis agree, and have put their name to a petition to halt this Sunday's cull.
As well as this, more than $100,000 has been raised in the last few days in a bid to stop the cull.
But Sage said National's petition shows the party "doesn't understand conservation".
"The previous government did not ensure that the limits in the Himalayan Tahr Control Plan, from 1993, were kept, and numbers of Tahr have ballooned three times higher than allowed."
She said National was "missing in action" while the Tahr population grew rapidly when it was in Government.