A defiant Donald J. Trump suggested on Sunday that he had been singled out for attacks by the hosts of last week’s widely watched Republican presidential debate and again threatened a third-party White House bid if he was not treated “reasonably fairly” by party leaders.

In a rapid-fire series of phone interviews with four Sunday television news programs, Mr. Trump defended his record on women’s issues, arguing that his real estate company had been among the first to put women in charge of major construction projects and that he had “always had a great relationship to the women.” He continued his criticism of the moderators of the debate on the Fox News network saying that no other candidate had been subjected to similarly tough questioning.

And he struck back at critics of his remarks about Megyn Kelly, one of the Fox moderators, which had resulted in his invitation to a meeting of conservatives in Atlanta on Saturday being rescinded. He said that his appraisal of Ms. Kelly’s motives for questioning him sharply during the debate — that she had “blood coming out of her wherever” — was being misconstrued by his rivals as a reference to menstruation in an effort to dampen his surge in the Republican primary. He had made similar remarks, he told more than one interviewer, about her co-moderator, Chris Wallace.