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.”