Three GOP Senators were in the meeting on immigration - two of them, Sen. Tom Cotton (R-AR) and Sen. David Perdue (R-GA) issued a joint statement on Friday afternoon, which did not expressly deny the incident.
"In regards to Senator Durbin’s accusation, we do not recall the President saying these comments specifically but what he did call out was the imbalance in our current immigration system," the two Senators said.
The third GOP Senator there was Sen. Lindsey Graham (R-SC), who - without relating the exact details of the President's remarks - said they were not proper.
"Following comments by the President, I said my piece directly to him," Graham said in a written statement. "The President and all those attending the meeting know what I said and how I feel."
The arc of this latest controversy followed a similar pattern from others involving President Trump over the past year - Democrats expressed outrage and demanded an apology, while most Republicans talked about something else.
But a few GOP voices did raise objections.
"It is completely inappropriate for the President to refer to other countries in the manner in which he reportedly did," said Rep. Erik Paulsen (R-MN).
"Unacceptable," added Rep. Brian Fitzpatrick (R-PA).
"If the White House will not deny the reports regarding the degradation of other nations and their peoples, it is necessary for the President to apologize immediately," said Rep. Carlos Curbelo (R-FL).
"Language like that shouldn't be heard in locker rooms and it shouldn't be heard in the White House," said Rep. Ileana Ros-Lehtinen (R-FL).
Back in his home state of Wisconsin, Speaker Paul Ryan was asked about the controversy, and told of how proud he was of his own family's trek from Ireland to the United States.
As criticism of the President grew, Mr. Trump was holding a ceremony to honor Dr. Martin Luther King, Junior - the federal holiday which bears his name is on Monday.
After the ceremony at the White House, reporters shouted questions at Mr. Trump, which included, "Mr. President, are you a racist?"
The President did not respond, and left the room after shaking hands with some of those in attendance.
Mr. Trump will spend the weekend at his Mar-a-Lago retreat in Palm Beach, Florida.