WASHINGTON — President Trump said on Thursday that he had not considered firing Robert S. Mueller III, the special counsel investigating Russian meddling in the election, contradicting private statements the president has made to his aides and friends about his desire to dismiss Mr. Mueller.

Mr. Trump spoke about the special counsel in a wide-ranging briefing with reporters at his golf club in Bedminster, N.J., where he also characterized as tepid his relationship with Attorney General Jeff Sessions (“It’s fine”) and shared his reaction to reports that Mr. Mueller’s investigators searched the home of his former campaign chairman, Paul Manafort (“I thought it was pretty tough stuff to wake him up, perhaps his family was there”).

The Justice Department investigation into possible links between Mr. Trump’s associates and Russia’s election interference has engulfed the White House in political and legal scrutiny. The revelation that Mr. Trump asked the F.B.I. director, James B. Comey, to end the inquiry into his first national security adviser, Michael T. Flynn, prompted the appointment of Mr. Mueller as a special counsel in May. And the president’s public scoldings of Mr. Sessions in recent weeks have prompted speculation that he is seeking a path to end the investigation.

Asked about the possibility of firing Mr. Mueller, the president said on Thursday: “I haven’t given it any thought. Well, I’ve been reading about it from you people. You say, ‘Oh, I’m going to dismiss him.’ No, I’m not dismissing anybody. I mean, I want them to get on with the task.”