WASHINGTON — Hillary Clinton’s remark at a fund-raiser that half of Donald Trump’s supporters fit into a ‘‘basket of deplorables’’ prompted a swift and negative reaction Saturday from Republicans, including denunciations and calls for her to apologize.

In response, the Democratic candidate for president Saturday said she regretted using the term “half’’ but stood by her depiction of her opponent appealing to fringe hate groups.

The comments the night before echoed an accusation that Clinton had levied previously — that Trump appeals to and amplifies racist, xenophobic, and anti-Semitic viewpoints. But Clinton triggered a fresh controversy by saying ‘‘half’’ of Trump’s supporters fit that description.

At a key moment in the campaign, when both candidates are trying to sharpen their focus for the final, post-Labor Day sprint, Clinton’s remarks took attention from Trump’s spate of gaffes and also from her own effort to turn the public’s attention to her qualifications for office and vision for the nation.

‘‘You know, to just be grossly generalistic, you could put half of Trump’s supporters into what I call the ‘basket of deplorables.’ Right?’’ Clinton said to applause and laughter from supporters at the LGBT for Hillary fund-raiser Friday night in New York that also featured a performance by Barbra Strei-sand. ‘‘The racist, sexist, homophobic, xenophobic, Islamophobic — you name it.’’

She continued: ‘‘He has given voice to their websites that used to only have 11,000 people — now have 11 million. He tweets and retweets their offensive, hateful, mean-spirited rhetoric.

‘‘Now, some of those folks — they are irredeemable, but thankfully they are not America.’’

Condemnation came swiftly from Trump’s allies and from the candidate himself, who on Twitter called the remarks ‘‘so insulting’’ and predicted that Clinton would pay a price in the polls.

In a statement issued later Saturday, Trump said that Clinton’s ‘‘true feelings’’ had come out. ‘‘How can she be President of our country when she has such contempt and disdain for so many great Americans?’’ Trump said. ‘‘Hillary Clinton should be ashamed of herself.’’

Trump’s campaign manager, Kellyanne Conway, called for Clinton to apologize, something that Trump himself has not done in the face of controversy.

Indiana Governor Mike Pence, Trump’s running mate, also weighed in, comparing Clinton’s remarks to President Obama’s controversial 2008 comments about people who ‘‘cling to guns or religion.’’ Pence said that such statements should preclude her from being elected president.

Others compared the remark to 2012 Republican nominee Mitt Romney’s infamous ‘‘47 percent’’ comment. Even if the comparison was imprecise — at most, Clinton’s comments referred to about one-quarter of the electorate — the Trump campaign has already sought to use the comparison to further define Clinton in the remaining months of the campaign.

Pointing out the similarities, Trump retweeted a September 2012 post from the Obama campaign’s Twitter account in response to Romney’s comment: ‘‘RT if you agree: We need a President who is fighting for all Americans, not one who writes off nearly half the country.’’

In 2012, Trump defended Romney’s ‘‘47 percent’’ comments.

In his remarks, recorded at a private fund-raiser, Romney asserted that 47 percent of voters ‘‘will vote for the president no matter what’’ because they are ‘‘dependent upon government,’’ ‘‘believe that they are victims,’’ and ‘‘pay no income tax.’’ The former Massachusetts governor was widely criticized for giving the impression that he was writing off half the country because of their economic status.

Clinton issued a statement Saturday saying that she regretted using the word ‘‘half’’ to describe the Trump supporters she was referring to.

‘‘That was wrong,’’ Clinton said. ‘‘But let’s be clear, what’s really ‘deplorable’ is that Donald Trump hired a major advocate for the so-called ‘alt-right’ movement to run his campaign and that David Duke and other white supremacists see him as a champion of their values.’’

In the statement, Clinton blasted Trump specifically for his feud with the family of a Muslim American Army officer who died in Iraq, his attacks against a Hispanic federal judge hearing two cases against him, and his prominent role in the ‘‘birther’’ movement promoting the idea that Obama was not born in the United States.

In her remarks at the fund-raiser, Clinton also called for empathy for the other ‘‘half’’ of Trump’s supporters.

‘‘That other basket of people are people who feel that the government has let them down, the economy has let them down, nobody cares about them, nobody worries about what happens to their lives and their futures, and they’re just desperate for change,’’ Clinton said. ‘‘It doesn’t really even matter where it comes from.

‘‘Those are people we have to understand and empathize with as well,’’ she added.

In an election cycle that has been more characterized by Trump’s controversies, Clinton’s comments represent a reversal of fortune. The flap also comes as polls show Trump narrowing Clinton’s lead nationally and in battleground states.

Since he installed new campaign leadership about three weeks ago, Trump has softened his tone on the campaign trail and mostly stuck to prepared rally speeches loaded onto teleprompters.

That level of discipline seemed to fade Friday night during a rally in a packed arena in the Florida Panhandle.

Trump said that as president, he would shoot Iranian boats out of the water if they make improper ‘‘gestures’’ toward American vessels, that Clinton is so protected from having to face consequences that she could murder someone in front of 20,000 witnesses and not face prosecution, and that voters need to be ‘‘very, very vigilant’’ on Election Day.