It was just one sentence, uttered to reporters who had gathered around Representative Ilhan Omar of Minnesota last week when she turned up at a Columbia University encampment to offer a show of support for pro-Palestinian protesters — among them, her daughter, a student activist — demonstrating against the Israeli attacks on Gaza.

Ms. Omar, one of the leading pro-Palestinian voices in Congress, rejected the argument that the protests were antisemitic, noting that many of the participants were Jewish. “All Jewish kids” should be kept safe, she said, no matter which side they were on in the debate — or, as she framed it, “whether they’re pro-genocide or anti-genocide.”

But with her formulation that Jews who support the Israeli military campaign are “pro-genocide,” Ms. Omar plunged into what has become an increasingly turbulent storm for many on the American left as it confronts questions about the extent to which antisemitism is shadowing demonstrations that have broken out on campuses from New York to Los Angeles.

Ms. Omar is a Democrat and one of two Muslim women in the House, and she was elected with the endorsement of, among others, President Biden.

“That phrasing is despicable,” said Rabbi David Wolpe, a visiting scholar at Harvard Divinity School, who resigned from a Harvard antisemitism panel after the university was swept by protests against Israel.

“I don’t know anyone who is pro-genocide,” said Mr. Wolpe, who said he was walking by an encampment at Harvard as he spoke on his cellphone. “In the course of condemning antisemitism, it displays antisemitism. Which is an astonishing paradox — I mean it’s a sad paradox.”

The remarks by Ms. Omar were the latest example of how the war in the Middle East has proved to be an agonizingly difficult issue to navigate across the political spectrum, but particularly on the left, which has split from the Democratic Party’s long history of support for Israel.

Some of the critics of Israel have appeared to struggle to distinguish opposition to the policies of the Israeli government under Benjamin Netanyahu, the prime minister, and what many Jewish leaders see as antisemitism unleashed over the past six months, which, in their view, has fueled many of the protests. Jewish students have said they felt threatened by the demonstrations on many campuses.

Ms. Omar showed no signs of pulling back on her statement, citing reports of threats against Muslims since the Hamas attack that set off the war. She pointed to an article in The Intercept reporting that students at the University of Massachusetts at Amherst had yelled out “Kill All Arabs.” In a post on X, she said: “This is the pro-genocide I was talking about, can you condemn this like I have condemned antisemitism and bigotry of all kind?”

The fact that there are Jews protesting against Israel at Columbia should be no surprise: It reflects the ideological diversity of American Jews on this issue. Many Jews, like many protesters at campuses from Columbia to the University of Southern California, are critical of the attacks launched by the Netanyahu government that have resulted in so many civilian casualties — while remaining firmly supportive of the existence of the Jewish state.

Ms. Omar’s remarks seemed to further polarize an already polarizing issue. “It is abhorrent that a sitting member of Congress would slander an entire group of young people in such a cold, calculated manner,” Jonathan Greenblatt, the executive director of the Anti-Defamation League, said on social media. “This is how people get killed.”

And it appeared to put some of her allies on the left in an uncomfortable position, including Senator Bernie Sanders of Vermont. When Mr. Sanders was asked on CNN if he was “comfortable” with what she said, he responded: “Look, what I think the essential point that Ilhan made is that we do not want to see antisemitism in this country. And I think the word genocide is something that is being determined by the International Court of Justice.”

In her remarks at Columbia, Ms. Omar said that it was “really unfortunate that people don’t care about the fact that all Jewish kids should be kept safe, and that we should not have to tolerate antisemitism or bigotry for all Jewish students, whether they are pro-genocide or anti-genocide.”

Her communications director, Jacklyn Rogers, said Ms. Omar had “clearly condemned antisemitism and bigotry for all Jewish students.”

“Attempts to misconstrue her words are meant to distract from the ongoing violence and genocide occurring in Gaza and the large antiwar protests happening across our country and around the world,” Ms. Rogers said.

All this showed few signs of lowering temperatures. Mr. Wolpe criticized Ms. Omar for trying to invoke the presence of a small group of Jewish demonstrators to rebut what he said was strong evidence of antisemitic sentiment at the demonstrations.

“This is a characteristic maneuver that I am not surprised to hear from Omar,” he said. “I think a lot of the students at the encampment are genuinely decent. But there is definitely a core that are not.”