“In show-business parlance, Donald Trump is a show runner,” said Al Cross, a longtime Kentucky political journalist who has known Mr. McConnell for more than 30 years. “He’s all about the show — it’s all about getting good ratings for Donald Trump — and McConnell has never been about the show. He’s all about business.”

Mr. Trump mentioned in an aside at the news conference that he would soon outline an economic development plan, though he confessed that he had yet to tell Mr. McConnell about it.

Despite pledges by both men that they share the same agenda, any good will that may have once existed dissolved after the Senate twice failed to repeal the Affordable Care Act. After the first defeat in July, Mr. Trump tweeted in August: “Can you believe that Mitch McConnell, who has screamed Repeal & Replace for 7 years, couldn’t get it done.”

In another tweet in August, he said, “The only problem I have with Mitch McConnell is that, after hearing Repeal & Replace for 7 years, he failed!”

Privately, Mr. Trump has repeatedly denigrated Mr. McConnell, most recently unloading about the Senate Republican leader during a dinner this month with a group of about a dozen conservative movement leaders in the Blue Room of the White House. According to two people with knowledge of the president’s remarks, he called Mr. McConnell “a weak leader” and said that he remained befuddled at Mr. McConnell’s inability to wrangle the votes needed to repeal the Affordable Care Act.

For his part, aides to Mr. McConnell say that he has been deeply frustrated by Mr. Trump’s willingness to lash out, even as the Senate leader successfully guided the chamber to confirm Mr. Trump’s cabinet and judicial nominations, including the president’s choice of Neil M. Gorsuch to the Supreme Court.

Soon after Mr. Trump took office, Mr. McConnell told associates that the new president had no clear sense of where he stood on most core issues, and he predicted that steering Mr. Trump — and taking the lead on policy — would be relatively easy.