WASHINGTON — Two members of President Trump’s cabinet appeared to retreat on Sunday from one of Mr. Trump’s signature campaign promises: to “immediately terminate” an Obama administration executive order meant to protect the legal status of children of undocumented immigrants.
“We’re not targeting them,” Homeland Security Secretary John F. Kelly said of such children in an interview on CNN’s “State of the Union.”
In a separate interview, on ABC’s “This Week,” Attorney General Jeff Sessions affirmed that the federal government did not “have the ability to round up everybody.”
“These people are caught between the law,” Mr. Kelly said on CNN, adding that “the president obviously is sympathetic.“
“But,” he added, “I just wish these kind of issues were dealt with legally by the United States Congress.”
Mr. Sessions made a similar observation in the ABC interview.
“There’s no doubt the president has sympathy for young people who were brought here at early ages,” he said. The administrations’s “first and strongest priority,” Mr. Sessions added, was the “criminal element.”
Mr. Trump said in February that he would approach Mr. Obama’s Deferred Action for Childhood Arrivals, or DACA, program “with heart,” calling the so-called dreamers it affects “absolutely incredible kids.”
“I have to deal with a lot of politicians, don’t forget, and I have to convince them that what I’m saying is — is right,” Mr. Trump said at the time. “The existing law is very rough. It’s very, very rough.”
On Friday, Mr. Trump told The Associated Press that undocumented immigrants brought here as children can “rest easy,” and that his agenda was “not after the dreamers; we are after the criminals.”
Mr. Trump had a more nationalist posture during the campaign. “I want dreamers to come from this country,” he said in February 2016. “We’re always talking about dreamers for other people. I want the children that are growing up in the United States to be dreamers also.”
Mr. Sessions was resolute on Sunday in arguing that the United States needed a more exacting immigration policy.
“Many of these are involved in criminal enterprises, hauling drugs and that kind of thing,” he said. “We need to end that. And then we’ve got to wrestle with what to do about people who have been here a long time.”
The Trump administration has continued to issue work permits to dreamers, but it also has moved to hasten the hiring of border agents. And the Justice Department recently sent letters to officials in jurisdictions known as “sanctuary cities,” threatening them with the loss of federal aid if they failed to cooperate with federal immigration authorities.
In a lawsuit filed last week, immigrant advocates accused the federal government of deporting for the first time an undocumented immigrant who had been allowed to stay in the country under the DACA program. Customs and Border Protection arrested the 23-year-old immigrant in California in February.
On Sunday, Mr. Kelly and Mr. Sessions also addressed the accompanying problem of financing a wall on the Mexican border that Mr. Trump has vowed to build. The current congressional funding bill expires on Friday, and Mr. Trump has made the wall a fulcrum of his new budget proposals.
On Sunday, Mick Mulvaney, Mr. Trump’s budget director, and Reince Priebus, the president’s chief of staff, said they were confident that the Republican-controlled Congress would approve the president’s plan.
“No one foresees or wants a shutdown next week,” Mr. Mulvaney said on “Fox News Sunday.” When pressed on whether Mr. Trump would accept a budget that did not include money for the border wall, Mr. Mulvaney said, “We don’t know yet.”
Mr. Priebus, appearing on NBC’s “Meet the Press,” said, “It’ll be enough for us to move forward through the end of September for us to get going on the wall.”
When asked whether he believed that the federal government would remain open past this week, Mr. Priebus said, “I believe it will.”
Later on Sunday, after those interviews, Mr. Trump wrote on Twitter that “Democrats don’t want money from budget going to border wall despite the fact that it will stop drugs and very bad MS 13 gang members.”
In another message posted a few minutes later, he wrote, “Eventually, but at a later date so we can get started early, Mexico will be paying, in some form, for the badly needed border wall.”
Republicans from areas where the wall would be built appear hesitant about Mr. Trump’s plans to pay for it. A survey last week by The Wall Street Journal found that the $1.4 billion price tag for the first portion of the wall is not supported by any member of Congress who represents territory along the southwest border.
There were recriminations on Sunday from allies of Mr. Trump. When some congressional Republicans balked at supporting health care legislation the president supported, he deployed Mr. Mulvaney to threaten several of them with primary opponents.
Republican Mark Sanford, Republican of South Carolina, confirmed as much while appearing on “State of the Union” on Sunday.
“I think that those kinds of threats are counterproductive,” Mr. Sanford said. “It all, I guess, fits in love, war and politics. But I don’t think it’s particularly productive to his own legislative agenda, and we’ll see what comes.”