The mailer, sent out days before the May 8 convention, showed pictures of Lee above a Mormon church temple and GOP U.S. Sen. Bob Bennett above the U.S. Capitol. It asks, "Which candidate really has Utah values?"
Utah is home to The Church of Jesus Christ of Latter-day Saints, and about 60 percent of the state is Mormon, including both Lee and Bennett.
Some Republican delegates found the mailer offensive and thought Lee's campaign was behind it, according to a delegate survey by Brigham Young University.
Lee, who had gone into the convention as the front-runner, finished in second place behind businessman Tim Bridgewater. Those two face off in a primary next week; Bennett finished third, ending his re-election bid.
Lee believes the mailer hurt his chances of victory at the convention.
The mailer is only identified as being paid for by the Utah Defenders of Constitutional Integrity, which is not a federally registered political action committee.
Lee's campaign has denied any involvement. On Tuesday, The Salt Lake Tribune reported that former Bennett aide and lobbyist Tim Stewart helped coordinate the mailer.
"I sincerely wish that I could take credit for what may be the most brilliant and possibly the biggest single game-changing political play in Utah politics in the last 20 years. But I can't. I am not that diabolical nor creative," he told the newspaper. "Instead, I am just a two-bit, wannabe political consultant, contacted by some Utah folks wanting to exercise their First Amendment rights. They came up with a great idea and we found a vendor and that's about the extent of it."
A message left with Stewart by The Associated Press was not immediately returned.
Utah Republicans chastised Stewart for his involvement. On his Facebook page, state GOP chairman Dave Hansen wrote that the mailer "was the childish product of Tim Stewart and his childish friends."
"Now stay out of Utah politics," Hansen wrote.
Jonathan Reid, Lee's campaign manager, said the complaint would be filed in the next few days.
"We are anxious to get to the bottom of who he refers to as this Utah group that directed him to issue the mailer," he said.
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