Donald J. Trump’s suggestion that a Fox News journalist had questioned him forcefully at the Republican presidential debate because she was menstruating cost him a speaking slot Saturday night at an influential gathering of conservatives in Atlanta. It also raised new questions about how much longer Republican Party leaders would have to contend with Mr. Trump’s disruptive presence in the primary field.

Continuing his complaints about Megyn Kelly, one of the moderators of the debate, in an interview on CNN Friday night, Mr. Trump said, “You could see there was blood coming out of her eyes, blood coming out of her wherever.” The remark prompted Erick Erickson, the leader of RedState, the conservative group, to disinvite him.

“If your standard-bearer has to resort to that,” Mr. Erickson told hundreds of conservative activists in a packed Atlanta hotel ballroom on Saturday, “we need a new standard-bearer.”

With Mr. Trump at center stage Thursday in Cleveland, Fox News shattered television viewership records for a primary debate: Nearly 24 million people watched. But any hopes that Mr. Trump, the real estate developer and television celebrity, would try to reinvent himself as a sober-minded statesman, or that he would collapse under scrutiny and tough questions, vaporized in the opening minutes when he refused to rule out running as an independent candidate for president. His remarks Friday only furthered the impression that he also had no intention of speaking more carefully. Mr. Trump denied on Saturday that he had been implying that Ms. Kelly was menstruating. “I think only a degenerate would think that I would have meant that,” he said in an interview, insisting that he had been referring to Ms. Kelly’s nose and ears.