Vukasovic, a local party treasurer, runs a hunting shop in Nybro in south-eastern Sweden.
This week photos from hunting trips to Africa began circulating on social media that show him posing with a lion, a giraffe and hippo he had hunted and killed.
Many commenters were furious at a perceived lack of respect for the animals, but Vukasovic was unrepentant.
“I've eaten 80 percent of the animals I've killed, including the lion in the picture,” he told newspaper Aftonbladet.
“The tastiest meat I've ever eaten, and will ever eat, is giraffe,” he added.
Vukasovic, who organizes hunting trips, said the photos were taken in South Africa and that the hunt was 100 percent legal.
“Hunting certain animals benefits people and benefits the animal. Previously hunting rhino hunting was banned, and now suddenly they've permitted it and there's a reason for that," he told the newspaper.
He added that the local authorities allowed hunting in areas where animals were starving due to a lack of food and water.
Commenters on his Facebook page however called him a “disgrace to Sweden” and a “caveman”.
When The Local reached Vukasovic by phone on Tuesday he said he didn't have time to talk:
“I have customers in my shop right now. They're much more important to me than you.”
The Sweden Democrats said on Tuesday they were looking into the matter before deciding whether to take any action.