SALT LAKE CITY -- Independent presidential candidate Evan McMullin said Wednesday he won't wither under attacks by white supremacists backing Donald Trump as his late campaign surge pushes him closer to winning Utah.

McMullin said at the University of Utah that the rise of Republican Donald Trump this campaign has illustrated a lingering problem in the United States with bigotry, racism and misogyny.

"When we have a presidential candidate who brags about grabbing women by their private parts and brags about how he can get away with it because he's famous, we still have a problem with sexism," McMullin told university students. "When one of our major parties is offering up a leader who thinks that way and speaks that way and who attacks people based on the colour of their skin or their faith... that tells us something about where we are."

McMullin has a chance to win enough conservative votes in Utah to defeat Trump and become the first non-Republican to win the state in nearly a half century, polls show.

At the event, he pointed to a Ku Klux Klan-affiliated newspaper this week running an editorial praising Trump, and a robo call placed in Utah against him by a white nationalist Trump supporter this week.

The Trump campaign denounced both. White nationalist William Johnson on Wednesday cancelled his robo call, apologizing for a "mean-spirited message" that included calling McMullin a "closet homosexual."

McMullin called them "baseless" lies earlier this week. His spokeswoman Rina Shah said in a statement Wednesday in response to the apology that the damage has already been done since the robo calls ran since Monday.

Shah reasserted the campaign's belief that Trump's campaign was behind the "desperate whisper campaign" and called on Trump to apologize. Trump's spokeswoman Hope Hicks has said Trump had no knowledge of the robo call and condemned the message.

"Not every Trump supporter is racist, but from the alt-right to the Ku Klux Klan, every racist in America has seemingly flocked to Trump's cause," Shah said in the statement.

His event at the university, in which he took questions from students, came a day after some of Utah's top Republicans, including Sen. Orrin Hatch, urged their fellow conservatives to unite around Trump rather than leave the party to vote for McMullin. Hatch said Trump "doesn't take any crap from anybody," and "he's exactly what we need."

Other top Utah Republicans, including U.S. Rep. Mia Love, Sen. Mike Lee and Gov. Gary Herbert have said they will not vote for Trump.

Utah's mostly-Mormon voters have widely rejected Trump's brash demeanour and taken exception to the billionaire's comments about women, minorities and Muslims. Trump finished a distant third in the March presidential caucus and polls show he's in a tight race with McMullin despite Utah being a Republican stronghold that hasn't elected a non-GOP presidential candidate since 1964.

McMullin, a Mormon and former CIA agent, tells voters around the state that a win for him in Utah would help launch a new conservative movement that is more inclusive and open to people of all faiths and races than Trump's Republican Party.

"The best thing we can do is stand up and fight for people being attacked based on their race, their religion, their gender," McMullin said. "Let's stand up and fight for equality."