"This is such a controversial issue ... so personally I can't and won't support it," he said.
Supporters said Lee deserved to be recognized because of his contributions to the city he helped found, The Spectrum of St. George reported.
"His statue will give members of this community the opportunity to discuss a great member of this community, in my opinion," said George Staheli, president of the Washington City Historical Society and a former history teacher.
But opponent Bill Stolz praised the council's vote.
"He did many fine things for this community, but he also committed mass murder, which was premeditated and resulted in the death of men, women and children," he said. "I'm amazed this is even up for discussion."
Cast in 2004 by artist Jerry Anderson, the 7-foot statue was supposed to be placed outside government buildings in Washington. City leaders commissioned the likeness for $35,000, but changed their minds in response to complaints from people who said it was inappropriate to pay tribute to a killer.
The controversy over Lee prompted the statue to be kept in storage for five years before being purchased by Lee descendants, who backed the latest request to display it at the original proposed location.
The site features statutes of four other area founders, with one pedestal that stands empty where the Lee statue was supposed to be located.
Anderson said he has cast dozens of faces in bronze from the anonymous American Indian warrior to President Lincoln and inventor Albert Einstein but none has stirred controversy like his likeness of Lee.
"There is too much controversy, and I try to stay out of that," he told The Spectrum. "It will be interesting to see what finally happens with (the statue)."