Megyn Kelly, one of the hosts of Thursday night's debate, questioned him over his years of anti-women remarks. The question infuriated Mr Trump.
"You could see there was blood coming out of her eyes, blood coming out of her - wherever," he said after the debate, speaking on CNN.
Ms Kelly, one of Fox News's most popular presenters, has a significant Republican following and the Politico website asked whether Mr Trump's comments could finally damage him.
"So picking a fight with Kelly - as Trump did when he chided her during a tough debate question about insults he's lobbed at women, dissed her in the spin room, and tweeted his complaints about her - carries risks that Trump's other feuds do not."
Hours later, the leader of the annual Red State Gathering in Atlanta announced on Twitter that Mr Trump was no longer welcome at the weekend event - and Miss Kelly was asked to join the conference in his place.
Almost universal support that "Trump won the debate." Only @FoxNews is consistantly fighting the Trump win, and I got them the ratings!
— Donald J. Trump (@realDonaldTrump) August 8, 2015
Re
Megyn Kelly quote: "you could see there was blood coming out of her
eyes, blood coming out of her wherever" (NOSE). Just got on w/thought
— Donald J. Trump (@realDonaldTrump) August 8, 2015
Wow,
CNN just said that Donald Trump won the DEBATE, connected best with
audience. Also, Time, Drudge, Newsmax, N.Y.Times and more!
— Donald J. Trump (@realDonaldTrump) August 8, 2015
"I have rescinded my invitation to Mr Trump. While I have tried to give him great latitude, his remark about Megyn Kelly was a bridge too far," said Erick Erickson, the organiser.
"His comment was inappropriate. It is unfortunate to have to disinvite him. But I just don't want someone on stage who gets a hostile question from a lady and his first inclination is to imply it was hormonal. It just was wrong."
"I mean, come on, you're going to accuse Megyn Kelly of having her period and that's why she asked the tough questions ... I just think that's crap."

