“Anyone who knows me knows these words don’t reflect who I am,” Mr. Trump continued.

“I said it, I was wrong, and I apologize,” he said.

Oddly, Mr. Trump seemed to frame his comments not as sincere concern about those he may have hurt or offended, but as part of his own journey, describing his growth as a person and how humbling it has been for him to campaign across the nation and learn of other people’s worries and travails.

“I’ve traveled the country talking about change for America, but my travels have also changed me,” he said, describing meeting mothers who have lost children and people who have lost their jobs.

“I pledge to be a better man tomorrow and will never, ever let you down,” Mr. Trump said.

Grudging though they seemed, Mr. Trump’s comments were a marked departure from his lifelong resistance to any admission of fault. Mr. Trump values strength and power and disparages weakness. His usual response, when criticized or hurt, has been to counterpunch forcefully.