Mr. Williams peppered Mr. Carson with questions about his plans for the department, while Mr. Harvey, who recently faced criticism for meeting with Mr. Trump during the transition, asked if Mr. Carson planned to “really put some real help” into struggling neighborhoods.

There was no mention of Mr. Trump’s proposal to cut his department’s budget by $6.2 billion and eliminate several programs aimed at providing and maintaining affordable housing for low-income Americans. Instead, Mr. Carson talked vaguely about removing blight across the country, focusing on the development of children and encouraging wealthy Americans to help low-income communities.

Mr. Carson also said that he wanted the private sector to get involved in issues like rethinking how abandoned buildings around the country are used.

“We are all in the same boat, and if part of the boat sinks, eventually, the rest of it goes down, too,” Mr. Carson said. “When the Titanic started going down, you could be in the most luxurious suite, but you are still going down. So, you need to recognize that there is a problem here, and you need to work on it, too.”

Mr. Harvey hit on what he called a novel approach to raising the issue of poverty, saying it would be best to call people “capital” to make the point that they are valuable. “I like calling people capital, because you know what? It makes people who are capitalists pay attention a little bit better,” he said. “If I looked at everybody as a stack of money, I could love them so easy.”