In a precursor to Mr. Carson’s woes, Mr. Trump has acknowledged embellishing a claim about himself in two books he wrote. As he described his financial comeback, Mr. Trump claimed that his debts had reached $9 billion in the 1990s. But in the 2007 deposition, Mr. Trump conceded that the figure was incorrect. (“That is a mistake,” he said, “and I don’t know how it got there.”)

Such fact-bending has extended to his campaign for president. During the last Republican presidential debate, Mr. Trump denied that he had called Senator Marco Rubio of Florida the “personal senator” of Facebook’s chief executive, Mark Zuckerberg, an advocate of immigration reform. Mr. Trump’s own campaign website had, in fact, described Mr. Rubio that way.

In television interviews on Sunday, Mr. Carson emphatically defended himself against claims that he had embellished his life story and expressed disappointment in Mr. Trump’s remarks.

“What does it say about people who immediately jump on the bandwagon if they hear something bad rather than waiting and finding out what the truth is?” Mr. Carson asked on ABC’s “This Week.”

Asked what it told him about people like Mr. Trump, he replied, “I would not be anxious to have a commander in chief who acted that way.”