Instead, he used a speech to the National Guard Association of the United States to defend his supporters at length, arguing that they were right to be concerned about border security and crime, and that those concerns did not indicate a hateful view of racial and religious minorities.  “If Hillary Clinton will not retract her comments in full, I don’t see how she can credibly campaign any further,” Mr. Trump said, demanding an apology. He claimed that his campaign was doing “amazingly well with African-American and Hispanic workers.”  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.  “People use the word ‘racist’ consistently to describe him,” Mr. Garin said. “But they also talk about him as a dangerous egomaniac.”  Still, on a conference call with top supporters Monday, advisers to Mr. Trump spoke of Mrs. Clinton’s turbulent stretch as a source of relief: For the first time in a while, they said, they were starting the week on offense, according to people who participated in the call who spoke on condition of anonymity about a private discussion. Campaign surrogates were told to hammer Mrs. Clinton for her description of Trump voters, and to say as little as possible about her pneumonia diagnosis.  Lt. Gen. Michael T. Flynn, a retired Army officer who advises Mr. Trump, said there was optimism in the campaign that the momentum of the race had “totally shifted in Mr. Trump’s favor.” He predicted that voters would see a distinction between “a guy who made all kinds of comments as he was fighting to win the primaries” and the Donald Trump of the general election.  Mr. Trump has taken other steps in recent days to steady his candidacy, moving to shore up his campaign in crucial swing states. With Mrs. Clinton holding a daunting advantage on the Electoral College map, Mr. Trump aimed a new television campaign at the four most critical states for his candidacy: Pennsylvania, Florida, Ohio and North Carolina.  He has given his aides greater leeway in directing his television advertising, allowing the campaign to focus on that smaller cluster of states, a change from as recently as two weeks ago, when Mr. Trump was personally choosing where to run television ads, according to two people briefed on the Trump operation.  Mr. Trump also removed the head of his Florida operation last week, replacing her with Susie Wiles, a veteran Republican operative close to Gov. Rick Scott. And Corey Lewandowski, Mr. Trump’s former campaign manager, who is still a trusted adviser, has visited New Hampshire in recent weeks, meeting with senior Republicans there and making suggestions on spending and strategy decisions in the state, two people familiar with his activities said.  It remains to be seen if Mr. Trump and his allies can maintain this level of determined focus. Numerous times, Mr. Trump has briefly adopted a more disciplined pose on the campaign trail, only to give in quickly to the temptation to taunt and brawl.  Even on Monday morning, as he refrained from taunting Mrs. Clinton in a television interview, Mr. Trump made an offhand reference to Senator Elizabeth Warren of Massachusetts as “Pocahontas.” Ms. Warren, a Democrat, has described herself as having Native American heritage.  Some of Mr. Trump’s advisers have suggested in the past that Mrs. Clinton’s health should be fair game. Blaise Ingoglia, the chairman of the Florida Republican Party, said he considered Mrs. Clinton’s handling of her health a legitimate campaign issue because she did not immediately disclose that she had pneumonia.  “The disturbing part of that whole thing is that the campaign is willing to conceal that instead of being up front and honest,” he said. “You really start to question: What else is being concealed?”
Mr. Trump scrambled to put his rival on the defensive, showing unusual restraint over her illness but denouncing her charge that many of his supporters were bigoted.