WEST PALM BEACH, Florida — Sen. Tom Cotton said Sunday that Senate Minority Whip Richard J. Durbin is spreading a false story about President Trump saying the U.S. does not need more immigrants from “sh — hole countries” such as Haiti and El Salvador.

Mr. Cotton, Arkansas Republican, said Mr. Durbin “has a history of misrepresenting” such private meetings, which are not customarily recorded.

“I certainly didn’t hear what Sen. Durbin has said repeatedly,” Mr. Cotton said on the CBS’ “Face the Nation.” “Sen. Durbin has a history of misrepresenting what happens in White House meetings, though, so perhaps we shouldn’t be surprised by that.”

He was referring to the Obama administration contradicting Mr. Durbin’s account of a 2013 meeting in which he claimed then-House Republican leader Eric Cantor told President Obama, “I cannot even stand to look at you.”

At the time, White House press secretary Jay Carney said it didn’t happen, but Mr. Durbin, Illinois Democrat, never backed down from his account.

Mr. Cotton, who attended the Oval Office meeting last week on immigration, said Mr. Durbin got it wrong this time, too.

Mr. Trump himself denied making the closed-door meeting remarks, which was first reported by The Washington Post, tweeting that “the language used by me at the DACA meeting was tough, but this was not the language used.”

He elaborated that he “never said anything derogatory about Haitians other than Haiti is, obviously, a very poor and troubled country. Never said ‘take them out.’ Made up by Dems. I have a wonderful relationship with Haitians. Probably should record future meetings — unfortunately, no trust!”

At least two Republicans at the meeting, Sen. David Perdue of Georgia and Homeland Security Secretary Kirstjen Nielsen, also said Sunday they did not hear the president use the word sh—hole.

“I don’t recall him saying that exact phrase,” Ms. Nielsen told Fox News.

Mr. Perdue was more emphatic in an interview on the ABC News program “This Week.”

“I’m telling you he did not use that word, George. And I’m telling you it’s a gross misrepresentation. How many times do you want me to say that?” he told host George Stephanopoulos.

Senate Minority Leader Charles E. Schumer said Mr. Cotton and Mr. Perdue were out of line.

“To impugn @SenatorDurbin’s integrity is disgraceful. Whether you agree with him on the issues or not, he is one of the most honorable members of the Senate,” the New York Democrat wrote on Twitter.

Sen. Lindsey Graham, South Carolina Republican, was also at the meeting, and he backed Mr. Durbin’s version of events.

The account pushed by Mr. Durbin spurred an outpouring of complaints that the president is a racist. Mr. Durbin said as much when Mr. Trump denied using the vulgar expression, saying the president “said things which were hate-filled, vile and racist.”

“We now know that we have in the White House someone who could lead the Ku Klux Klan in the United States of America, somebody who could be the leader of the Neo-Nazi,” Rep. Luis Gutierrez, Illinois Democrats, said on MSNBC.

Rep. Cedric Richmond, chairman of the Congressional Black Caucus, and Rep. Jerrold Nadler, ranking Democrat on the House Judiciary Committee, said they will attempt to censure the president this week.

“The President’s bigoted fearmongering is not acceptable and his remarks completely warrant total condemnation and censure from Congress,” they said in a joint statement.

Two Democratic lawmakers — Reps. John Lewis of Georgia and Maxine Waters of California — announced they would boycott Mr. Trump’s State of the Union speech later this month.

“I think he is a racist,” Mr. Lewis said Sunday on ABC’s “This Week” program. “In good conscience, I cannot and will not sit there and listen at him as he gives the State of the Union Address.”

Mr. Lewis also led dozens of Democrats in boycotting Mr. Trump’s inauguration last year.

California Attorney General Xavier Becerra, a Democrat, said on “Fox News Sunday” that “in every respect, what he is showing is he is a racist.”

“Let me put it to you this way: mental instability, mendacity, now bigotry — having the combination, that’s lethal” for the nation, he said.

Some other Republicans defended Mr. Trump without denying that he might have said what was reported.

“I think it’s unfair to sort of paint him, ‘Oh well, he’s a racist,’ when I know for a fact that he cares very deeply about the people of Haiti because he helped finance a trip where they would get vision back for 200 people in Haiti,” Sen. Rand Paul, a Kentucky Republican who is an ophthalmologist, said on NBC’s “Meet the Press.”

He said the comments were not constructive, “but I also think that, to be fair, we shouldn’t draw conclusions that he didn’t intend.”

• Ben Wolfgang contributed to this report.

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