Mr. Walters apologized on Twitter on Friday night. “I spoke with Mike Steele and apologized because the words I used do not capture my heart,” he wrote.

He added: “Sometimes when you speak, the words that come out do not reflect what’s intended. Many of us were critics of how Chairman Steele performed at the R.N.C. He is a good man, and he did his best.”

In a phone interview on Saturday morning on Ms. Reid’s show, Mr. Steele was asked if the Republican Party had a problem with racism.

“Yes, they do. And I think we need to be honest and acknowledge it,” Mr. Steele said. “The fact that people sit here now and say this has nothing to do with race — yeah, it does, when you stand on a podium and blatantly speak to race the way Ian did.”

Mr. Walters did not respond to a request for comment on Saturday.

Michael Ahrens, a spokesman for the Republican National Committee, said in a statement, “We reject the offensive comments made” on Friday night.

Black people made up 2 percent of registered Republican voters in 2016, according to the Pew Research Center, the same percentage as in 1992. President Trump received 8 percent of the black vote in 2016.

Mr. Steele, speaking Saturday on his show on SiriusXM radio with Matt Schlapp, the chairman of the American Conservative Union, said comments like Mr. Miller’s “undermine” efforts to “expand this party and its reach into communities of color across the country.”