Following the lead of rivals Ron Paul and former Utah Gov. Jon Huntsman, GOP hopeful Mitt Romney said Tuesday he will not take part in billionaire Donald Trump’s Dec. 27 debate.

Mr. Romney told Fox News he will skip the Trump-moderated Iowa debate that has been criticized by some Republicans as a distraction and potential embarrassment.

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Republican strategist Karl Rove, appearing on Fox News Monday, said: “[Trump] could do a lot of damage to somebody and I suspect it’s not gonna be to the candidate that he’s leaning towards. This is a man who says himself that he’s going to potentially run for president of the United States starting next May. Why do we have that person moderating a debate?”

Sen. John McCain on Tuesday also questioned the wisdom of the GOP identifying its candidate with Mr. Trump:

“There are too many debates and we have lost the focus on from what the candidates’ vision for America is to who’s going to make a mistake … I don’t think it’s helping the Republican Party or our candidates,” the 2008 GOP presidential candidate said on Fox.

Mr. Trump, a New York real estate magnate and reality television star who considered his own run for the 2012 Republican presidential nomination earlier this year, has responded to the criticism by calling Mr. Paul and Mr. Huntsman “joke candidates” and referring to Mr. Rove as a “political hack.’

Mr. Trump created a buzz earlier this year with a pro-Trump, anti-Obama media blitz in which he hammered on questions about the president’s birth certificate.

Mr. Paul and Mr. Huntsman earlier declined to participate in the debate, sponsored by hosted by Newsmax and ION Television, but GOP candidates Newt Gingrich and Rick Santorum have said they will take part.