President Trump received a phone call from Elon Musk late on Monday night, outreach that led to a public expression of regret by the billionaire early Wednesday for the attacks he had lodged against the president in their extraordinary public showdown last week, according to three people briefed on the conversation.

The call came after the tech entrepreneur spoke privately on Friday with Vice President JD Vance and the White House chief of staff, Susie Wiles, about a path to a truce. Ms. Wiles told associates she had come to like working with Mr. Musk and was one of his regular points of contact. The people spoke on the condition of anonymity to describe the private discussions.

Those conversations paved the way for the strikingly chastened tone Mr. Musk struck in an X post early Wednesday, in which he wrote: “I regret some of my posts about President @realDonaldTrump last week. They went too far.”

Representatives of Mr. Trump and Mr. Musk did not respond to requests for comment.

Asked by reporters Wednesday evening if he felt he was in a better place after Mr. Musk’s outreach, the president was noncommittal. “I really haven’t thought too much about it,” he said as he arrived with the first lady, Melania Trump, at the John F. Kennedy Center for the Performing Arts for an opening night performance of “Les Misérables.”

For his part, Mr. Vance told reporters that he could not recall if he spoke with Mr. Musk last week. “But yes, I have spoken to Elon and the president about trying to ensure that Elon is publicly supporting and privately supporting the president’s agenda,” the vice president added as he arrived for the show.

Mr. Musk had spent several days signaling that he wanted to make up with the president after the two men engaged in a sharp series of personal attacks last Thursday that played out from the Oval Office and on social media.