The Housing and Urban Development Secretary said he "did not want to get into an argument about who's done the most" during his appearance on ABC's "This Week" with George Stephanopoulos.
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Carson, the only African American cabinet secretary in the Trump administration, instead listed the president's successes in supporting the black community, such as pushing for prison reform and restoring funding for the nation's historically black colleges and universities.
Stephanopoulos continued to press Carson, asking if the president should stop making the comparison.
"It's hard to compare that with Lyndon Johnson passing the Civil Rights Act, the Voting [Rights] Act, Ulysses S. Grant sending in troops to take on the Klu Klux Klan, President Eisenhower sending in troops to enforce Brown v. Board of Education," Stephanopoulos said.
Carson said it's an "important thing for us to acknowledge what has happened in the past."
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"We should be willing to look at what we've done together, collectively, to make progress," he said.
The president's claim during a one-on-one interview with Fox News came after weeks of racial tension following the death of George Floyd.
Earlier this week, Trump was criticized for scheduling his first campaign rally since the coronavirus outbreak on June 19 in Tulsa, Oklahoma. That date is Juneteenth, the commemoration of the ending of slavery in the United States, and Tulsa has its own troubling history on race.
The president has since rescheduled the rally.