Senator Kirsten Gillibrand of New York, who presented herself in the presidential race as a champion of women and families, said Wednesday that she was withdrawing from the Democratic primary after failing to qualify for a third debate next month — a development she described as fatal to her candidacy.

Ms. Gillibrand said in an interview that she would endorse another candidate in the primary but had not yet picked a favorite. Though she stopped short of saying she would endorse a woman, Ms. Gillibrand, who has made electing women to Congress a personal cause, said the next president had to be capable of uniting the country and suggested that a woman might be best suited for the job.

“I think that women have a unique ability to bring people together and heal this country,” Ms. Gillibrand said, adding, “I think a woman nominee would be inspiring and exciting.”