John Swallow, who will take office Jan. 7, said he's concerned about domestic abuse, fraud and child abuse, but will not as attorney general prosecute "otherwise law-abiding partners, The Salt Lake Tribune reported Saturday.
Nationwide, there are about 38,000 people in polygamous relationships, many in Utah.
Swallow said Utah can't afford to prosecute all polygamous participants or deal with consequences from those relationships, adding he will continue the policies on polygamy of his predecessor, Mark Shurtleff.
Swallow said he will defend a challenge to the state's polygamy ban.
Some anti-polygamy activists say the state could do more to battle abuses within polygamous groups.
"I definitely have felt frustration and anger of what I feel has been ignored for way, way too many years ... the abuse in the guise and name of religion," Kristyn Decker, who spent her childhood in the Apostolic United Brethren and wrote the book "50 Years in Polygamy," said.