“When you were confronted about this accusation, you said you were, quote, not a church boy, and that you, quote, have so many skeletons in my closet. You then texted Miss Cooney an apology and indicated you had no memory of what you described,” Ms. Murray said, asking pointedly whether he had made sexual advances.

“No, I did not,” Mr. Kennedy said. He added that the account had been debunked, without offering information to substantiate his claim. Ms. Murray asked why he had apologized. “I apologized for something else,” he replied.

(In the text, whose contents were reported by news organizations including The Times in July, Mr. Kennedy wrote, “I have no memory of this incident, but I apologize sincerely for anything I ever did that made you feel uncomfortable or anything I did or said that offended you or hurt your feelings.”)

Ms. Murray pressed on, asking Mr. Kennedy if there were “any other instances where you have made sexual advances toward an individual without their consent? Just yes or no.”

“No,” Mr. Kennedy replied.

In the answers he submitted on Friday, he did not specify the type of settlement he had reached, or the nature of the “misconduct or inappropriate behavior” of which he was accused. In an email statement to The Times on Friday, Ms. Murray recalled the exchange over the babysitter, and said that Mr. Kennedy was “patently unfit” to lead the Department of Health and Human Services.

“His answers to the finance committee are deeply troubling — the American people deserve answers, and senators must have them before a vote is held on his nomination,” the statement said.