WHITE PLAINS, N.Y. (AP) -- Hillary Clinton said Saturday that she was wrong to put half of Donald Trump's supporters in a "basket of deplorables," but she didn't back down from describing his campaign as largely built on prejudice and paranoia. The Republican accused her of a "grotesque attack on American voters."

Less than 24 hours after she made the comments at a private New York City fundraiser, Clinton said in a statement, "last night I was 'grossly generalistic' and that's never a good idea. I regret saying 'half' — that was wrong." But she argued that the word "deplorable" was reasonable to describe much of Trump's campaign.

"He has built his campaign largely on prejudice and paranoia and given a national platform to hateful views and voices, including by retweeting fringe bigots with a few dozen followers and spreading their message to 11 million people," the Democratic nominee said.

Responding in a statement, Trump said it was "disgraceful that Hillary Clinton makes the worst mistake of the political season and instead of owning up to this grotesque attack on American voters, she tries to turn it around with a pathetic rehash of the words and insults used in her failing campaign?"

Trump added that Clinton was showing "bigotry and hatred for millions of Americans," arguing that she was "incapable to serve as President of the United States."

Clinton, who has said she is the candidate to unify a divided country, made the "deplorables" comment at an LGBT fundraiser Friday night at a New York City restaurant, with about 1,000 people in attendance. She has made similar comments recently, including on an Israeli television station.

"To just be grossly generalistic, you could put half of Trump's supporters into what I call the basket of deplorables. Right? The racist, sexist, homophobic, xenophobic, Islamaphobic — you name it," she said, before stressing that other Trump supporters are frustrated and need sympathy.

Trump and his supporters quickly pounced on the remark, arguing that it revealed Clinton as disconnected from struggling Americans.

"Wow, Hillary Clinton was SO INSULTING to my supporters, millions of amazing, hard-working people. I think it will cost her at the polls!" Trump said in a tweet.

Running mate Mike Pence, in remarks at the Values Voter conference in Washington, shot back: "The truth of the matter is that the men and women who support Donald Trump's campaign are hard-working Americans, farmers, coal miners, teachers, veterans, members of our law enforcement community, members of every class of this country who know that we can make America great again."

Of course, while Clinton is taking heat for her comment, Trump's brand is controversy. At a rally in Pensacola, Florida, on Friday, he said Clinton is "so protected" that "she could walk into this arena right now and shoot somebody with 20,000 people watching, right smack in the middle of the heart. And she wouldn't be prosecuted."

Clinton's rhetorical stumble came as the candidates head into the final two months of the campaign, with Trump trying to make up ground before the Nov. 8 election.

Clinton has not let the media into many private fundraisers, but press was allowed in to hear her remarks Friday. At the New York restaurant, Clinton bemoaned the people she described as "deplorables," saying "unfortunately there are people like that. And he has lifted them up. He has given voice to their websites that used to only have 11,000 people — now how 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," said Clinton, who was the country's top diplomat during President Barack Obama's first term.

Clinton then pivoted and tried to characterize the other half of Trump's supporters, putting them in "that other basket" and saying they need empathy.

She described them as "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."

Seeking to explain the statements, Clinton spokesman Nick Merrill said in a series of tweets after the remarks that Clinton has been talking about the "alternative right," or "alt-right" movement, which often is associated with efforts on the far right to preserve "white identity," oppose multiculturalism and defend "Western values." Merrill argued that "alt-right" leaders are supporting Trump and "their supporters appear to make up half his crowd when you observe the tone of his events."

But the moment recalled comments about voters — also at private fundraisers — that have tripped up presidential nominees in the past.

Weeks before the 2012 election, Republican Mitt Romney landed in hot water for saying that 47 percent of the public would vote for President Barack Obama "no matter what" because they depended on government benefits and his job was "not to worry about those people."

During the 2008 Democratic primary, then-Sen. Obama said that small-town voters "cling to guns or religion or antipathy to people who aren't like them or anti-immigrant sentiment or anti-trade sentiment as a way to explain their frustrations."

On Saturday, Clinton's staff said she attended another fundraiser at the Armonk, New York, home of attorney David Boies. But reporters traveling with her campaign were not allowed in and did not see her.

Trump, meanwhile, did not address Clinton's comment at his only scheduled public appearance on Saturday, a funeral in St. Louis for social conservative activist Phyllis Schlafly.

Trump noted that Schlafly rooted for the underdog, and "the idea that so-called little people, or the little person that she loved so much, could beat the system — often times, the rigged system."