The Aug. 2 dinner at the Bridgehampton, N.Y., home of Howard Lutnick, the Cantor Fitzgerald chief executive, was a high-powered affair. Among the roughly 130 people who dined under an air-conditioned tent were some of Donald Trump’s wealthiest supporters, including the billionaire hedge-fund financier Bill Ackman, who sat next to the former president, and Omeed Malik, the president of another fund, 1789 Capital.

Some guests hoped Mr. Trump would signal that he was recalibrating after a series of damaging mistakes. He did not.

Before the dinner, answering a question that voiced concerns about the upcoming election during a small round-table discussion inside Mr. Lutnick’s house, Mr. Trump said, “We’ve got to stop the steal,” reviving yet again his false claims about the 2020 election — claims that his advisers have urged him to drop because they don’t help him with swing voters.

According to two people present, Mr. Trump himself also brought up his remark, made two days earlier at a gathering of the National Association of Black Journalists, in which he had questioned Vice President Kamala Harris’s racial identity.

It had been a display of flagrant race-baiting that was egregious even by Mr. Trump’s standards, and it instantly reprogrammed America’s TV news chyrons: He falsely claimed that Ms. Harris had only recently decided to identify as Black for political purposes.

But Mr. Trump showed no regret. “I think I was right,” he told the rattled donors that Friday night.