Mr. Trump’s statement of regret, in a prepared speech in which he spoke of a “New American Future,” seemed to be a step toward trying to recover from a number of public quarrels and other episodes that have damaged his campaign, including a dispute with the family of an American Muslim soldier who was killed in Iraq.

But in his speech, which he read off a teleprompter, he did not specify what he regretted, offer specific apologies or linger on the subject. In his campaign, Mr. Trump has at times sounded restrained and on-message, only to quickly revert to his more pugilistic nature.

Hillary Clinton, the Democratic nominee, had previously warned about the prospect of Mr. Trump trying to change his ways, concerned that voters who had been turned off by his inflammatory comments on a variety of subjects might look favorably on any tempering of Mr. Trump’s tone.

“There is no other Donald Trump,” Mrs. Clinton said at an event in Florida this month. “What you see is what you get.”

The rally here was Mr. Trump’s first since he announced new leadership on Wednesday for his struggling campaign, the second overhaul in the last two months.