But Mr. Trump, who records little support in the polls among racial minorities and educated whites, did not address any of the past remarks that have contributed to his low standing with those groups. He has continued to call for a crackdown on immigrants who are in the country illegally, and has declined to retract his false assertions in the past that President Obama was not born in the United States. Mr. Trump has also not expressed regret for clashing with the family of a slain Muslim Army captain or renounced his proposal to bar Muslims from entering the country.

Mrs. Clinton has rebuked Mr. Trump over the last month for what she has called his promotion of racially insensitive messages and policies and his alignment with leaders of the movement known as the “alt-right,” which is widely seen as holding fringe and racist views.

Robert Blizzard, a Republican pollster, said that Mr. Trump appeared to be recovering his footing in the race, but that it might be too late for him to change many voters’ longstanding assessment of his character and capabilities.

“Hillary Clinton clearly won the summer, and there’s little doubt Donald Trump dug himself a very deep hole in the aftermath of the nominating conventions,” Mr. Blizzard said. “While Trump is starting to climb out of that hole now, his ability to take advantage of a few bad weeks for Clinton is going to be limited due to enduring views about his judgment, his temperament and his rhetoric toward other ethnicities and women.”

And Democrats are skeptical that Mr. Trump will be able to reinvent himself by using Mrs. Clinton’s biting comments as a shield. Geoff Garin, a Democratic pollster who advises a pro-Clinton “super PAC,” described an exercise he uses in focus groups, asking voters to write down three words to describe Mr. Trump before the discussion begins.