The president of Harvard, Claudine Gay, is facing the biggest test of her career, as the university’s governing board met behind closed doors on Monday amid calls for her removal.

Dr. Gay and the leaders of the University of Pennsylvania and M.I.T. came under attack for their testimony in a congressional hearing last week on campus antisemitism. The presidents faced blowback for what were seen as lawyerly, evasive answers about whether students should be disciplined if they called for the genocide of Jews.

Penn’s president, Elizabeth Magill, resigned on Saturday, and pressure was mounting at Harvard, with dueling letters both supporting Dr. Gay and calling for her ouster.

Here are some key points to know about Dr. Gay and what led to this moment.

Dr. Gay, 53, took office in July, becoming the first Black president and the second woman to lead Harvard.

The daughter of Haitian immigrants, she earned an undergraduate degree in economics from Stanford University — where she would later teach — and a Ph.D. in government from Harvard.

She joined Harvard’s faculty in 2006, serving as a professor of government and of African and African American studies. She became dean of Harvard’s Faculty of Arts and Sciences in 2018.

Her appointment as university president was seen as both history-making and timely.

Dr. Gay, a supporter of diversity in hiring and an expert on minority representation and political participation in government, took the reins just as the Supreme Court rejected the use of race-conscious admissions at Harvard and other universities around the nation.

She was selected from a pool of more than 600 nominations.

Penny Pritzker, senior fellow of the Harvard Corporation, who led the presidential search committee, praised Dr. Gay at the time for her “a rare blend of incisiveness and inclusiveness,” bringing both a “bedrock commitment to free inquiry and expression, as well as a deep appreciation for the diverse voices and views that are the lifeblood of a university community.”

Dr. Gay testified last week along with Ms. Magill and Sally Kornbluth, the president of the M.I.T., in a hearing that House Republicans convened to address issues of bias against Jewish students. Harvard, like other campuses, has been roiled by demonstrations and confrontations between pro-Israel and pro-Palestinian students in the weeks since the Oct. 7 Hamas attack in Israel, and Israel’s subsequent invasion of Gaza.

In one exchange, Representative Elise Stefanik, Republican of New York, pressed Dr. Gay over whether the university condoned chants of “intifada” on its campus — an Arabic word that means “uprising” and is heard by many Jews as a call for violence against them.

“That type of hateful speech is personally abhorrent to me,” Dr. Gay said. She appeared to try to walk a tightrope, noting that Harvard was committed to free expression, “even of views that are objectionable, offensive, hateful,” while also saying that speech that crossed a line into bullying and harassment would be dealt with.

Later, Ms. Stefanik asked: “Does calling for the genocide of Jews violate Harvard’s rules of bullying and harassment? Yes or no?”

Dr. Gay replied, “It can be, depending on the context.” She added: “Antisemitic rhetoric, when it crosses into conduct that amounts to bullying, harassment, intimidation, that is actionable conduct, and we do take action.”

Dr. Gay apologized in an interview with The Harvard Crimson, the campus newspaper, published last week.

“I got caught up in what had become at that point, an extended, combative exchange about policies and procedures,” Dr. Gay said. “What I should have had the presence of mind to do in that moment was return to my guiding truth, which is that calls for violence against our Jewish community — threats to our Jewish students — have no place at Harvard, and will never go unchallenged.”

As groups of donors, alumni and students pressed to oust Dr. Gay, about 700 members of Harvard’s faculty, in addition to hundreds more alumni, came to her defense in several open letters.

One, from Black faculty members, called the attacks on the president “specious and politically motivated.” The letter, which was drafted and signed by some of Harvard’s most prominent professors, said that Dr. Gay “should be given the chance to fulfill her term to demonstrate her vision for Harvard.”

A separate letter expressing “no confidence” in Dr. Gay was also gaining support on Monday. Signed by Harvard students and alumni, it urged her to resign or be fired. “It is not appropriate for Claudine Gay to serve as President of Harvard, as she does not represent our collective values or the Harvard that we have come to know,” that letter said.

The Harvard Corporation, the governing body that could decide Dr. Gay’s fate, has been quiet.

The situation differs in at least some respects from the one at Penn, where Ms. Magill — a newcomer at Penn after serving as provost at University of Virginia — had faced eroding support well before her testimony.