Trump was asked whether he would tell Republicans to stop using the “DEI” description, which many find offensive.
He asked Rachel Scott, an ABC News reporter, to define “DEI” and, asked whether he thought Ms Harris was a “DEI hire”, he said: “I mean, I really don’t know. Could be, could be. There are some.”
The White House condemned Trump’s comments. Karine Jean Pierre, the press secretary, called them “repulsive” and “insulting”, adding that “no one has any right to tell someone who they are”.
“She is the vice-president of the United States, Kamala Harris. We have to put some respect on her name, period,” Ms Pierre added.
Trump’s first-ever appearance at the convention triggered controversy before it began, with some senior members quitting the group in protest over the decision to invite him.
During the event, which at times became heated, he claimed he had done more than any other president for the black community since Abraham Lincoln, who abolished slavery.
“I think it’s disgraceful that I came here in good spirit. I love the black population of this country. I’ve done so much for the black population of this country,” said Trump.