By Luciana Lopez and Jeff Mason

NEW YORK (Reuters) - Democratic presidential candidate Hillary Clinton on Saturday said she regretted saying "half" of Republican rival Donald Trump's supporters belonged in a "basket of deplorables," but made no apologies for calling out "prejudice and paranoia" among Trump's campaign and supporters.

"Last night I was 'grossly generalistic,' and that's never a good idea. I regret saying 'half' - that was wrong," Clinton said in a statement, the day after comments at a fundraiser in New York.

But "Trump has built his campaign largely on prejudice and paranoia," she said, adding: "I won't stop calling out bigotry and racist rhetoric in this campaign."

Republicans and Trump supporters responded fiercely on social media to Clinton's remarks at the LGBT fundraiser and the episode threatened to distract from her efforts to paint Trump as unqualified for the presidency.

But Trump on Saturday sought to use Clinton's comments to make the same charge about her.

"How can she be President of our country when she has such contempt and disdain for so many great Americans?" a Trump statement asked.

"Hillary Clinton should be ashamed of herself, and this proves beyond a doubt that she is unfit and incapable to serve as President of the United States," he added.

At Friday night's fundraiser, Clinton said Trump had given voice to hateful rhetoric through his behavior as a candidate for the White House in the Nov. 8 election.

"To just be grossly generalistic, you can put half of Trump’s supporters into what I call the 'basket of deplorables,'" Clinton said. "Unfortunately there are people like that. And he has lifted them up."

Some of those were irredeemable, she said, but they did not represent America.

The other basket of Trump's supporters constituted individuals desperate for change who felt let down by the government and the economy, Clinton added.

"They don’t buy everything he says, but he seems to hold out some hope that their lives will be different," Clinton said. "Those are people we have to understand and empathize with, as well."

Trump's campaign hammered on Clinton throughout the day.

"Hillary Clinton’s low opinion of the people that support this campaign should be denounced in the strongest possible terms," Mike Pence, the governor of Indiana and Trump's running mate, said at the Values Voter Summit in Washington.

"So let me just say from the bottom of my heart: Hillary, they are not a basket of anything. They are Americans, and they deserve your respect."

Trump, a New York businessman who has never run for political office before, regularly says things that some consider insulting, racist or off-color. On Friday night, he told supporters in Pensacola, Florida, that Clinton could shoot someone and not be prosecuted.

"Because she's being so protected, 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, okay?" he said. [nL1N1BM031]

But Clinton's remarks got top billing on Twitter where the hashtag #BasketOfDeplorables was trending, with shows of condemnation and support for Clinton.

Twitter user Basketeer Vendetta, under the account Vendetta92429, tweeted a photo of Trump supporters wearing campaign T-shirts and hats, adding: "Proud to be part of the #BasketOfDeplorables with my fellow Americans."

And Trump himself tweeted: "Wow, Hillary Clinton was SO INSULTING to my supporters, millions of amazing, hard working people. I think it will cost her at the Polls!"

But some Twitter users agreed with Clinton, referencing remarks by Trump that have been called racist, such as when he described some Mexican immigrants drug dealers and rapists.

RISKY COMMENT

Clinton's comment could nevertheless end up being a boon to Trump.

"As long as Trump stays out of the way and doesn't overshadow Hillary's comment, her 'basket of deplorables' comment should dominate the media in the coming days and runs the risk of negatively defining her campaign," said Republican strategist Doug Heye.

Republican strategist Ana Navarro, who has been highly critical of Trump, said Clinton might have crossed an important line.

"When you are running for President, you are running to represent all Americans, even the ones you think are deplorable," said Navarro.

But Jamal Simmons, a Democratic consultant, said the remarks probably would not wrest voters from Clinton.

"We’re moving to the part of the election process where there’s a lot less persuasion of new voters and more persuasion of the people who like you to turn out and work to elect you," he added.

Many of Clinton's fundraisers have been closed to the media, but not the one on Friday night.

Some critics likened Clinton’s observation to 2012 Republican candidate Mitt Romney’s "47 percent" comment in which he said 47 percent of voters are dependent upon the government and would vote for President Barack Obama no matter what. His campaign struggled to recover after the remark leaked.

But Democratic strategist Jim Manley, who supports Clinton, pointed out that Romney was talking about all voters, and Clinton was specifically describing Trump supporters.

(Additional reporting by Steve Holland; Editing by Mary Milliken and Grant McCool)