President Trump said he would not overrule his acting attorney general, Matthew G. Whitaker, if he decided to curtail the special counsel investigation being led by Robert S. Mueller III of Russian interference in the 2016 presidential campaign.

“Look, it’s going to be up to him. . . . I would not get involved,” Trump said in an interview on “Fox News Sunday.”

The president also publicly mocked a House Democrat who criticized Whitaker, deriding Rep. Adam B. Schiff (Calif.) as “little Adam Schitt” in a tweet.

In the weeks since Trump forced Jeff Sessions to resign as attorney general and chose Whitaker to serve as his interim replacement, Whitaker has faced calls from Democrats to recuse himself from oversight of the investigation, given his previous criticism of the inquiry. Trump said in Sunday’s interview that he “did not know [Whitaker] took views on the Mueller investigation as such” before he appointed him.

Trump essentially shut the door to sitting down with Mueller, telling host Chris Wallace that his written answers mean “probably this is the end” of his involvement in the inquiry.

“I think we’ve wasted enough time on this witch hunt and the answer is probably: We’re finished,” Trump said. He said that he had given “very complete answers to a lot of questions” and that “that should solve the problem.”

Trump said Friday that he had answered written questions from Mueller “very easily.” The president told Wallace in Sunday’s interview that it “wasn’t a big deal” and that he expects his legal team to submit the answers “at some point very soon.”

Trump’s answers had long been sought by Mueller during the inquiry, which began 18 months ago. The investigation has led to charges against 32 people, including 26 Russians. Although four Trump aides have pleaded guilty to various charges, Mueller’s team has not indicated whether it thinks Trump associates conspired with Russians or whether the president obstructed justice by pressuring Justice Department leaders.

Key lawmakers also weighed in on Whitaker on Sunday.

In an appearance on ABC News’s “This Week,” Schiff, the incoming chairman of the House Intelligence Committee, said that Whitaker “was chosen for the purpose of interfering with the Mueller investigation” and that he “should have absolutely nothing to do” with the inquiry. Schiff also said Whitaker should be subject to Senate confirmation.

“He auditioned for the part by going on TV and saying he could hobble the investigation,” Schiff said, calling Whitaker’s appointment unconstitutional and “an attack on the rule of law.”

Trump fired back in a tweet Sunday afternoon in which he said that Mueller had not been confirmed by the Senate, either. However, Mueller, unlike the attorney general, is not a Cabinet-level official; he was appointed by Deputy Attorney General Rod J. Rosenstein, and his role does not require Senate confirmation.

Mueller was twice confirmed by the Senate to serve as FBI director — in 2001 and 2011.

“So funny to see little Adam Schitt (D-CA) talking about the fact that Acting Attorney General Matt Whitaker was not approved by the Senate, but not mentioning the fact that Bob Mueller (who is highly conflicted) was not approved by the Senate!” Trump said , misspelling Schiff’s last name.

The lawmaker responded sarcastically in a tweet: “Wow, Mr. President, that’s a good one. Was that like your answers to Mr. Mueller’s questions, or did you write this one yourself?”

Some Republicans on Sunday were focusing on Whitaker’s potential successor. Sen. Roy Blunt (Mo.) said on ABC’s “This Week” that Whitaker “seems to be a person who has the ability to do that acting job” but that the Justice Department needs a permanent leader as soon as possible.

Blunt, a member of the Senate GOP leadership who sits on the Intelligence Committee, said it would be a “huge mistake” for Trump to try to end the Mueller inquiry.

During Sunday’s wide-ranging interview, Trump said that he is thinking about replacing people in “three or four or five positions” in his administration and that of those, “maybe it’s going to end up being two.” He declined to say whether Chief of Staff John F. Kelly will remain in his job through 2020, as previously indicated, saying only, “I mean, it could be. Let’s see what happens.”

Trump praised Homeland Security Secretary Kirstjen Nielsen but also said he wants her to “get much tougher.” He has voiced dissatisfaction about Nielsen’s performance on immigration enforcement and has told advisers that he has decided to remove her in the coming weeks.

The president said that despite Republicans’ loss of at least three dozen seats in the House, their holding on the Senate was “historic” and “a tremendous victory.”

“I didn’t run. I wasn’t running. My name wasn’t on the ballot,” Trump said. During the months leading up to Election Day, he repeatedly told supporters at his Make America Great Again rallies to “pretend I’m on the ballot.”

Trump also said Sunday that he could not envision a situation in which he would try to amend the Constitution to run for a third term as president, in 2024.

“Just won’t happen,” he told Wallace. “I think the eight-year limit is a good thing, not a bad thing.”

Tory Newmyer, Carol D. Leonnig and Josh Dawsey contributed to this report.