[Which Democrats are leading the 2020 presidential race this week?]

Unlike some other frustrated candidates, she declined to complain about the Democratic National Committee’s qualifying rules for the debates: “I think the D.N.C. did the best they could,” she said.

Her exit from the presidential race represents an abrupt setback in a political career defined, up to this point, by a steady rise to prominence since her first election to Congress in 2006. A former corporate lawyer, Ms. Gillibrand won a conservative-leaning House seat in upstate New York, campaigning as a rural moderate with liberal views on health care but more conservative inclinations on gun rights and immigration.

When she joined the Senate in 2009, as an appointee to the seat Hillary Clinton vacated to take over the State Department, Ms. Gillibrand revised her stances on a number of issues to better match the politics of her deep-blue state. She quickly emerged as a champion of progressive causes including gay rights, paid family leave and fighting sexual assault in the military, and she became a formidable fund-raiser for Democratic campaigns.

Yet as a presidential candidate, Ms. Gillibrand found herself shunned by a class of powerful Democratic Party donors — who had once been supportive of her political ambitions — after she called on Al Franken of Minnesota to resign from the Senate amid allegations of groping and other sexual misconduct toward women. Ms. Gillibrand acknowledged in the interview that she had paid a political price but reiterated that she had no regrets about confronting Mr. Franken.

“We know there were donors who were angry about it and did not support me because of it,” Ms. Gillibrand said, adding, “I wouldn’t change what I did, because I would stand with those eight women again today.”