Federated Farmers have denied they are using the fire in Lake Ōhau as an excuse to push for free grazing.
Hundreds of people were forced to flee the area in Mackenzie Basin after the blaze broke out early on Sunday.
Fire crews are continuing to fight the fire, though strong winds on Tuesday have made for challenging conditions.
On Monday Federated Farmers said wilding vegetation on Department of Conservation (DoC) land had helped fuel the fire. But Conservation Minister Eugenie Sage hit back against that comment, saying nature didn't start fires.
"I think Federated Farmers are making a push for free grazing," Sage told RNZ.
But Federated Farmers High Country chairperson Rob Stokes on Tuesday called that comment a "cheap shot", saying a sensible discussion on the subject was needed.
"For Conservation Minister Eugenie Sage to suggest yesterday that Federated Farmers was opportunistic in the wake of the Ōhau blaze and just looking for free grazing was a cheap shot," Stokes said.
"We have been warning about fire fuel loads on DoC land in the South Island for years. We have only been opportunistic in the sense that the near-miss to human lives, not to mention the stock loss and serious property damage from Sunday's fire, was a chance to finally get some traction with the department and the Government on this issue.
"Farmers aren't looking for 'free' anything. They operate commercial businesses and they're looking for a partnership, with contracts, to try and reduce a serious risk to safety, private property and the environment."
Stokes said he recognised there were some areas of DoC land where it was "totally inappropriate" to have livestock, but said in less sensitive areas a low number of sheep or cattle could keep combustible grass, scrub and immature wilding pine levels down.
Rather than be beneficial for farmers grazing stock in such areas would actually be "more of a headache than a gain" due to the time-consuming nature of mustering, he said.
"Any grazing arrangement might only be for three months a year. What is the farmer supposed to do with the animals for the other nine months? That's why it's sensible to have long-term arrangements with land-owners immediately adjacent to DoC land, so there's no costs trucking animals in and so on," Stokes said.
"Federated Farmers welcomes an opportunity to sit down with DoC for a sensible discussion on the practicalities of fire fuel loads on the public estate."
DoC operations manager Karina Morrow on Monday said grazing on public conservation land would have a "significant negative impact on native species" and that "grazed tussock still burns very well, which is why stock are lost in fast-moving grass fires".