Representative Jeff Duncan of South Carolina

Mr. Duncan argued that a true condemnation would have made reference to Ms. Omar, and the comments that prompted the resolution.

Mr. Duncan stirred protests in 2017 when he posted on Facebook an image of a white man labeled “Europe” with a noose around his neck watering a small tree labeled “Islam,” with one end of the noose tied around it. “Chew on this picture,” he wrote.

“Jeff I know you’re not racist. Let’s put that to the side,” Bakari Sellers, a former Democratic legislator in South Carolina, tweeted in response. “But this is bigoted, ignorant and embarrassing.”

Representative Louie Gohmert of Texas

In a fiery speech on the House floor on Thursday, Mr. Gohmert complained that the resolution was “watered down.”

Mr. Gohmert dealt with his own accusations of anti-Semitism last year after he falsely accused Mr. Soros of collaborating with the Nazis during World War II, a popular myth on the far right. “George Soros is supposed to be Jewish, but you wouldn’t know it from the damage he’s inflicted on Israel, and the fact that he turned on fellow Jews and helped take the property that they owned,” he said on Fox Business Network.

Patrick Gaspard, the president of Mr. Soros’s Open Society Foundations, sent a letter to Mr. Gohmert in December demanding an apology for the “disturbing and false anti-Semitic slur.”