Hunters are prepared to restrict how far they can travel and who with to try persuade the government to permit the activity at Covid-19 alert level three.
New Zealand Pig Hunting Association said hunting was a low-risk activity for the spread of Covid-19, and was proposing conditions to mitigate any outstanding risk.
These included only hunting within the region people live, only going with people in their current bubble, not staying overnight, and having a detailed safety plan including a log of any people they come into contact with.
Executive member Geoff Fitzgerald said hunting was food gathering for many people.
"This time of the year, they thrive on getting their organic supplies of wild pork and venison."
There's almost no risk to spreading the virus while hunting, and not allowing it highlights a discrepancy with other permitted activities, such as surfing and mountain biking, he said.
"I'm sure there would be more accidents surfing and opportunity of spread than what there would be with someone hunting alone or with two people out in the bush."
The association supported similar calls by the Game Animal Council and Deerstalkers Association.
Landowners have told the association pigs are encroaching on their farms, and they need hunters to deal with them, Fitzgerald said.