Rudolph W. Giuliani, the president’s personal lawyer, was similarly dismissive of the idea that the attack on the congresswomen was racist. “He’s just pointing out that all they ever seem to do is attack America,” he said.

And Marc Short, chief of staff to Vice President Mike Pence, said Mr. Trump’s “intent” was not “in any way racist.” Mr. Short pointed to the fact that an Asian immigrant, Elaine Chao — who also happens to be married to Mitch McConnell, the Senate majority leader — serves in the president’s cabinet as transportation secretary. “This is not a universal statement that he’s making,” Mr. Short said. “He’s making it about an individual member of Congress.”

Neither the White House press secretary, Stephanie Grisham, nor one of Mr. Trump’s most visible television defenders, Kellyanne Conway, weighed in on Monday. And other White House officials acknowledged privately that Mr. Trump’s statements were difficult to defend.

But in interviews with a half-dozen current and former White House officials, many said Mr. Trump’s comments, which relied on an age-old taunt to further an us-against-them political strategy Mr. Trump hopes to ride into his re-election, did not at a “gut level” rise to the level of the Charlottesville crisis, in which one protester was killed. After that incident, Mr. Cohn even drafted a resignation letter, though he ultimately did not submit it to Mr. Trump.

More frustrating to many internally, they said, was that Mr. Trump interrupted an intraparty Democratic fight between Speaker Nancy Pelosi and the freshman congresswomen known as “the squad” by uniting them against a common enemy in the White House.

Administration veterans said they had long ago become immune to thinking anything Mr. Trump said would stick to him for more than one news cycle. Indeed, even a year after Charlottesville, Republican lawmakers who distanced themselves from the president had come back to embrace his tax overhaul and his selection of Brett M. Kavanaugh for the Supreme Court.