Fox News Channel moderators, from left, Chris Wallace, Megyn Kelly and Brett Baier in Cleveland at the first Republican presidential primary debate. (Aaron Josefczyk/Reuters)

Donald Trump said that he values women and that only a “deviant” would believe that he was referring to menstruation when he said that Fox News host Megyn Kelly had “blood coming out of her wherever” when she questioned him during Thursday's Republican presidential primary debate.

Trump, speaking Sunday on CNN’s “State of the Union,” sought to repair the damage wrought by his comment. The billionaire was disinvited this week from the RedState Gathering, an influential conservative event, amid a backlash that has raised questions about the future of his candidacy.

“When you’re negative on women’s health, you can forget about it,” he said. “I’m the exact opposite. I cherish women. I want to help women. I’m going to be able to do things for women that no other candidate would be able to do, and it’s very important to me.”

[Trump’s history of flippant misogyny]

Trump appeared on four Sunday shows to explain his statement, a sign of the wide interest generated by the controversy. In multiple instances, he declined to apologize to Kelly, arguing that he never meant to suggest that she had her menstrual period when she asked him pointed questions at the debate.

“I didn’t even finish the thought,” he said of his comment. “I was going to say nose and/or ears because that’s a very common statement … it’s a statement showing anger.”

“Only a deviant would say that what I said was what they were referring to. You almost have to be sick to put that together,” he added.

Trump, who told NBC's "Meet the Press" that it is hard for women to attack his looks "because I’m so good-looking," took pains to express respect for women. He criticized fellow GOP presidential contender Jeb Bush for saying earlier in the week that he was "not sure we need a half a billion dollars for women's health issues."

"I think he's got a huge problem," Trump told CBS's "Face the Nation." "Look, I am going to be very much up on the whole issue of women's health.  I mean, it's very important. To me, it's vital.  And when I heard him say that, I thought it was terrible."

[So which women has Donald Trump called ‘dogs’ and ‘fat pigs’? These ones.]

During an interview with ABC's "This Week," Trump called women "phenomenal."

"I've had such an amazing relationship with women in business," he said. "They are amazing executives. They are killers ... I have many executives that are women. They are doing a phenomenal job. I pay them a tremendous amount of money. They make money for me."

GOP presidential hopeful Carly Fiorina criticized Trump, telling CBS that women were "really sort of horrified" by his statement and that she had had to contend with similar insinuations during her time in the private sector.

“They were completely inappropriate and offensive comments, period,” she said Sunday on CNN.

“As I made my way up in the business world, I’ve had a lot of men imply that I was unfit for decision-making because maybe I was having my period. … Women understood that comment, and, yes, it is offensive,” she said.

Trump's GOP rivals roundly criticized his comments on Sunday, with Sen. Rand Paul (Ky.) calling them "vulgar" and Ben Carson pushing back on Trump's argument that he is simply refusing to be politically correct.

"In no way do I advocate, you know, saying mean things about people. That has nothing to do with political correctness," Carson said during an interview with CBS.

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