On Sunday night, in a video shown to the plenary session of a World Jewish Congress event in New York City, Mr. Trump gave his most extensive remarks so far about the atrocities of the Holocaust as evidence of his “passion” on the topic, what he called “the darkest chapter of human history.”

“We mourn, we remember, we pray and we pledge: never again. I say it, never again,” Mr. Trump said in the video. “The mind cannot fathom the pain, the horror and the loss. Six million Jews, two-thirds of the Jews in Europe, murdered by the Nazi genocide. They were murdered by an evil that words cannot describe, and that the human heart cannot bear.”

He added: “We must stamp out prejudice and anti-Semitism everywhere it is found. We must defeat terrorism, and we must not ignore the threats of a regime that talks openly of Israel’s destruction. We cannot let that ever even be thought of.”

The event was not a heavy lift for Mr. Trump — he and the group’s president, Ronald S. Lauder, are longtime friends. Matthew Brooks, the executive director of the Republican Jewish Coalition, nonetheless pointed to the video as a chance for critics to “take a moment and listen to what he has to say.”

“There’s no question that right now the professional class of complainers are going to find whatever reason they want to criticize and take issue with anything the president does. The fact of the matter is, I think he should strongly be applauded,” said Mr. Brooks, whose organization is heavily backed by the casino magnate Sheldon G. Adelson.

Mr. Brooks said that Tuesday’s appearance at the Capitol is a chance for Mr. Trump to put the “absurd” notion that he is “soft on anti-Semitism” to rest.

“Could some things have been said somewhat differently” during the campaign, Mr. Brooks asked, answering, “Yes.”

But others said that Mr. Trump’s appearance amounts to too little, too late. More than 2,500 people signed an open letter, within the first hour of its posting, to support a request by Bend the Arc Jewish Action asking the Holocaust museum to withdraw its invitation to Mr. Trump. Others went on Twitter to urge their followers to call the museum to register their protest.