Mr. Trump’s White House chief of staff, Mick Mulvaney, defended the president on the Sunday shows and insisted that there was nothing racist about his attack on Mr. Cummings’s district.

“Does the president speak hyperbolically? Absolutely,” he said on “Face the Nation” on CBS. “Have we seen this type of reaction for him before? Yes, and you will again because he pushes back. He fights back when he feels like he’s attacked, and what Mr. Cummings said this week was wrong.”

On “Fox News Sunday,” Mr. Mulvaney said Mr. Trump made a fair point about the state of affairs in Mr. Cummings’s district. “It has absolutely zero to do with race,” he said, adding: “Have you seen some of the pictures on the internet? Just this morning from the conditions in Baltimore, Md. Have you seen them?”

Baltimore has struggled with some of the highest crime rates in the country in recent years, but Mr. Cummings’s district, which is 53 percent African-American, also includes vast suburban stretches and has a median household income in the top half of congressional districts. City boosters popularized the hashtag #WeAreBaltimore to defend it against the president.

Some Republicans were left in the uncomfortable position of once again being asked to answer for the president. “Look, I didn’t do the tweets,” Senator Rick Scott of Florida said on “Meet the Press” on NBC. “I can’t talk about why he did what he did. But I’m very disappointed in the people, like Congressman Cummings, who is attacking Border Patrol agents that are trying to do their job.”

At a recent hearing, Mr. Cummings confronted Kevin K. McAleenan, the acting secretary of homeland security, about conditions for detained migrants, sharply criticizing the secretary’s contention that his department was doing its “level best” to manage the situation.

“What does that mean?” Mr. Cummings demanded. “What does that mean when a child is sitting in their own feces, can’t take a shower? Come on, man. What is that about? None of us would have our children in that position. They are human beings.”