But the dispute among the president’s defenders about the vulgarity he actually used did nothing to allay critics. “I think it’s all the same,” said Representative Cedric L. Richmond, Democrat of Louisiana and the chairman of the Congressional Black Caucus, which Mr. Trump also mentioned dismissively during the Oval Office meeting, according to one participant.
“The words don’t matter,” Mr. Richmond said. “The words just cement his sentiment that the people in those countries are less worthy, and he would like people from different countries. He chose the black countries to say he didn’t want those people and one of the whitest countries to say he did want them. I think that’s telling.”
Asked if he saw any difference between the two words, Senator Tim Scott of South Carolina, the only black Republican in the chamber, was equally dismissive: “No,” he said.
Aides to Mr. Trump, and allies of the administration, readily acknowledged that the president sprinkles most private interactions with profanity and rolled their eyes at suggestions that previous presidents did not use such language. They saw his main offense as using it in front of a Democrat — Senator Richard J. Durbin of Illinois, who was in last week’s meeting and on Tuesday again questioned the president’s defenders about the word they said was used.
“I can tell you explicitly they are wrong,” Mr. Durbin said in a CNN interview about the reports to the contrary. “And let me also say, is that their defense?”
The “Rashomon”-like perspectives that have come to define most group meetings with the president gave his aides something to seize on to muddy the issue. But after an initial nonresponse on Thursday, the day of the meeting — most White House aides were at a party for a departing National Security Council official, Dina H. Powell — the aides swung into action long after the story could be contained, a fact that aggravated Mr. Trump’s allies outside the building.
There were reports that the White House might have pressured senators to say that they heard something different. But just a few hours after the first reports of what Mr. Trump had said, Rich Lowry, of the conservative magazine National Review, said on CNN that he had been told the word was in fact “shithouse,” although people heard it differently because the other obscenity is more commonly used.
One person familiar with an account of the meeting from Senator Tom Cotton of Arkansas, who was there, said that the president did not use either word repeatedly, and that the context was his opposition to the type of immigration system that Mr. Durbin and Senator Lindsey Graham, Republican of South Carolina, seemed to be promoting.
Any harsh language was not specific to predominantly black nations, according to Mr. Cotton’s account, and Mr. Durbin never spoke up in protest during the meeting.
But there is no doubt that one person at the meeting who did was Mr. Graham.
Mr. Graham, who was there with Mr. Durbin in support of their immigration plan, challenged Mr. Trump after the president lamented that there were not more Norwegians or Asians seeking to emigrate to America, although precisely when he did it was not quite clear.
In an interview, Mr. Graham said that he responded to Mr. Trump’s complaints about Norwegians not migrating to America.
“The conversation was going down the wrong road, I thought,” he said. “Here’s how I started, I said, ‘If you’re from Norway, Mr. President, you’re a Norwegian.’ But if you’re from America what are you? It’s not an ethnic group, it’s not a religion — it’s an ideal. You can’t tell Americans by the way they look. People from all over the world want to be part of this ideal. And that diversity is our strength not our weakness.”
Testifying under oath before the Senate Judiciary Committee on Tuesday, Kirstjen Nielsen, the homeland security secretary, effectively confirmed that Mr. Graham had confronted Mr. Trump, a remarkable concession from one of the president’s own appointees.
“Senator Graham gave an impassioned speech on what he believes are the American ideals,” Ms. Nielsen said during questioning with Democrats on the panel.
Notably, Ms. Nielsen refused to go as far as denying Mr. Durbin’s account, which Mr. Cotton and Senator David Perdue, Republican of Georgia, effectively did on television on Sunday.
She insisted she had not heard Mr. Trump use either word but did not flatly deny that he had, even allowing that he had used “tough language.”
“Anything is possible,” Ms. Nielsen told Senator Amy Klobuchar, Democrat of Minnesota, when she asked if Mr. Trump had used one of the words.
And how about the other, Ms. Klobuchar asked?
“Again, it’s possible,” Ms. Nielsen responded.