Alveda King described Mr Trump as appearing "visibly moved" at two moments during his tour of the National Museum of African American History and Culture.
She told The Atlanta Journal-Constitution she heard Mr Trump say "Boy, that is just not good. That is not good," when he saw a stone auction block from Hagerstown, Maryland.
When they later came across a set of shackles used to restrain children, Mr Trump reportedly said: "That is really bad. That is really bad."
The US president was making his first visit to the new Smithsonian along with Ms King, Ben Carson, Senator Tom Scott and his daughter Ivanka.
After the tour, Mr Trump said: “Today and every day of my presidency, I pledge to do everything I can to continue that promise of freedom for African-Americans, and every American. Nothing is more important.”
“This tour was a meaningful reminder of why we have to fight bigotry, intolerance and hatred in all of its very ugly forms."
Ms King told the paper his visit sent a positive message to black Americans.
However, Janice Mathis, executive director of the National Council of Negro Women, said: “History is always instructive and the museum tells a powerful story, so it is unlikely that he wouldn’t be moved by his visit.
“Now, it is my hope that the visit will move beyond a celebration of Black History Month and that he will now consider public policy that is appropriate for a culturally and racially diverse nation today.”
The Independent has contacted the White House for a statement.
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