In an interview published Wednesday
, Trump told the New York Times that Rep. Elijah Cummings made the comments to him in the Oval Office.
"Elijah Cummings [a Democratic representative from Maryland] was in my office and he said, 'You will go down as one of the great presidents in the history of our country,'" Trump said.
"Really," replied NYT reporter Maggie Haberman, who also is a CNN political analyst.
"And then he went out and I watched him on television yesterday and I said, 'Was that the same man?'" the President said.
But Cummings -- a frequent Trump critic -- told CNN he had a different recollection of the conversation.
"During my meeting with the President and on several occasions since then, I have said repeatedly that he could be a great president if ... IF ... he takes steps to truly represent ALL Americans rather than continuing on the divisive and harmful path he is currently on," Cummings told CNN Thursday in a statement.
During a March meeting about prescription drug prices at the White House, Cummings offered Trump "a road map for changing his ways to help all Americans," according to Jennifer Werner, communications director for the House oversight committee's Democrats.
The advice included asking Trump to investigate voter suppression instead of voter fraud, back legislation to reduce the prices being charged for prescription drugs and "immediately stopping his horrible language about the black community" and "the immigrant community" among other issues.
"He told the President that if he represented all Americans, he would have tremendous potential and that he should start leading instead of tweeting," Werner told CNN.
While Cummings was one of the most high-profile Democrats who chose not to boycott Trump's inauguration, he has spoken out repeatedly against the President since then -- particularly about Trump's words and policies toward minorities.
This isn't the first time Trump has made a claim that Cummings has disputed.
In February, Trump accused
Cummings at a news conference of backing out of a meeting. Cummings responded at the time in a statement saying: "I have no idea why President Trump would make up a story about me like he did today."