President Trump said in an interview aired Sunday that he most likely would not sit for an interview with the special counsel, Robert S. Mueller III, asserting that “we’ve wasted enough time on this witch hunt and the answer is, probably, we’re finished.”

The president also claimed that he had no idea that his acting attorney general, Matthew G. Whitaker, viewed the Mueller investigation skeptically, despite reports that the two had multiple conversations about the inquiry over the past year.

The comments from Mr. Trump were made during a wide-ranging, sometimes testy interview with Chris Wallace, the host of “Fox News Sunday,” who sat with the president at the White House last week. The president continued to be defensive about his abandoned trip to an American military cemetery during a visit to Paris last week, insulted the widely respected retired Navy admiral who oversaw the raid that killed Osama bin Laden and said he declined to listen to an audio recording of the dissident journalist Jamal Khashoggi being killed by people connected to the Saudi crown prince last month.

His comments on the Mueller investigation marked an apparent reversal from a year of claiming that he was willing and eager to be interviewed by the special counsel, who is investigating possible collusion between the president’s campaign and Russian officials during the 2016 election. Mr. Trump’s legal team has blanched at the idea, fearing that the president might lie under oath, and has steadily narrowed the path for such an interview.