In his remarks to reporters, Mr. Scott made it clear he did not go to the White House for a photo op, but to decisively rebut Mr. Trump’s claim — to the president’s face — that “both sides,” racists and anti-racist protesters, were responsible for the violence that followed a torchlight protest against the removal of a statue of Robert E. Lee.

“My response was that, while that’s true, I mean I think if you look at it from a sterile perspective, there was an antagonist on the other side,” Mr. Scott said.

“However, the real picture has nothing to do with who is on the other side,” he said.

“It has to do with the affirmation of hate groups who over three centuries of this country’s history have made it their mission to create upheaval in minority communities as their reason for existence,” he continued. “I shared my thoughts of the last three centuries of challenges from white supremacists, white nationalists, KKK, Nazis. So there’s no way to find an equilibrium when you have three centuries of history versus the situation that is occurring today.”

Mr. Trump responded by repeatedly saying, “That makes sense,” and concluded the meeting by telling the senator, “Let’s keep talking.”

Mr. Scott’s version of the meeting was at odds with a description given to reporters by Sarah Huckabee Sanders, the White House press secretary, in the White House briefing room. When asked if Mr. Scott had expressed his “displeasure” at the president’s response to Charlottesville, she said, “Not at all,” adding that Mr. Scott and Mr. Trump had discussed “what we can do to bring people together, not talk about divisions within the country.”