WASHINGTON — When President Trump learned this week that his chief of staff, John F. Kelly, reportedly called him “an idiot” on several occasions, he expressed little in the way of frustration or anger, an uncharacteristically low-key response from someone with little tolerance for slights.

Attending a fund-raising dinner on Monday, Mr. Trump told a confidant that he did not believe Mr. Kelly would say something like that, a point he made directly to Mr. Kelly in the Oval Office not long after the comment was reported. It was “fake news,” the president concluded, an assessment that he repeated in a pair of tweets.

Many current and former officials said Mr. Trump’s response was less a vote of confidence in his top adviser than a sign of indifference — a reflection of the kind of cold truce that exists between two powerful and mercurial men who have grown tired and irritated with each other, but are in no immediate rush to part ways.

The president has come to believe that Mr. Kelly is hiding things from him, in the view of people who work in the White House and insist on anonymity to describe private conversations. He has complained that Mr. Kelly has not been forthcoming about the pasts of some staff members, who either opposed him during the 2016 presidential primaries or had connections to the Bush family. And he has taken to venting about Mr. Kelly to an array of friends and supporters, while expressing confidence that recent successes — such as the continued strength of the economy and progress toward nuclear disarmament talks with North Korea — are proof that he is his own best adviser.