The party is hoping to gather support in the Riksdag to gain influence over Swedish predator policies, the Swedish news agency TT reported.
The party has sparked a fiery debate between wolf defenders and critics on several online forums, the report said, causing a party founder, Gunilla Gronvall, to back away from the party's wolf-elimination stance.
"We want a zero-tolerance policy in populated areas of the countryside, let's put it that way. But to say that we want to shoot all wolves would be brutal," she said.
However, Nature Democratic head Marcus Werjefeldt said the original party stance hasn't changed.
"We don't want to eradicate wolves. We just don't want them in Sweden," he told TT.
Werjefeldt said he doesn't know how to keep all wolves out of the country, but maintains policies need to change.
"This is all about getting a new predator policy," he said.
The party leader said he was surprised the party has garnered so much attention.
"It can't be news that there are people who don't want wolves," he said.