Reno, Nevada (CNN) Hillary Clinton issued a blistering takedown of Donald Trump Thursday, accusing him of racism and arguing that "fringe" elements have taken over the Republican Party.

"From the start, Donald Trump has built his campaign on prejudice and paranoia," Clinton said at a campaign rally here. "He's taking hate groups mainstream and helping a radical fringe take over the Republican Party. His disregard for the values that make our country great is profoundly dangerous."

She added, "This is what I want to make clear today: A man with a long history of racial discrimination, who traffics in dark conspiracy theories drawn from the pages of supermarket tabloids and the far reaches of the Internet, should never run our government or command our military. Ask yourself: If he doesn't respect all Americans, how can he serve all Americans?"

The comments -- delivered in what could be a crucial swing state in November -- mark a dramatic escalation in the war of words between Clinton and Trump. The Republican nominee flatly labeled her a "bigot" on Wednesday, prompting Clinton to tell CNN he was "taking a hate movement mainstream" and was outside the norm of American politics.

Trump offered a prebuttal in New Hampshire earlier Thursday, saying that Clinton "paints decent Americans as racists."

"She bullies voters who only want a better future and tries to intimidate them out of voting for a change," Trump said at a campaign event in Manchester. "Hillary Clinton isn't just attacking me, she's attacking all of the decent people of all backgrounds -- doesn't matter -- of all backgrounds who support this incredible, once in a lifetime movement."

He later tweeted after her remarks, "Hillary Clinton's short speech is pandering to the worst instincts in our society. She should be ashamed of herself!"

Hillary Clinton's short speech is pandering to the worst instincts in our society. She should be ashamed of herself! — Donald J. Trump (@realDonaldTrump) August 25, 2016

Asked by WMUR in Manchester later Thursday if he wanted white supremacists to vote for him, Trump simply responded, "No. I don't at all."

'Alt-right'

Speaking at a community college, Clinton sought to link Trump to the "alt-right," an informal group of mostly white conservative men aligned with the Republican Party that sees Trump as the only choice in 2016. The "alt-right" lives primarily online, regularly pushing racist, homophobic and sexist content.

Trump, however, has been embraced by the fringe groups, in part because he tapped Steve Bannon, the former head of Breitbart News, as the CEO of his campaign. Bannon has said that his former publication is "the platform of the alt-right."

Clinton said the Bannon hire has led to a "de facto merger" between Breitbart and the Trump campaign represents a "landmark achievement" for a "fringe element that has effectively taken over the Republican Party."

"All of this adds up to something we've never seen before," Clinton said. "Of course there's always been a paranoid fringe in our politics, steeped in racial resentment. But it's never had the nominee of a major party stoking it, encouraging it, and giving it a national megaphone. Until now."

Outreach to Republicans

Clinton devoted large portions of her speech to making overtures to Republicans, calling this election "a moment of reckoning for every Republican dismayed that the party of Lincoln has become the party of Trump."

"This is not conservatism as we have known it. This is not Republicanism as we have known it," Clinton said, departing from her prepared remarks.

"We have our disagreements. We need good debates. Need to do it in respectful way. Not finger- pointing. Every day, more Americans are standing up and saying "enough is enough" -- including a lot of Republicans," Clinton said. "I'm honored to have their support. And I promise you this: With your help, I will be a president for Democrats, Republicans and Independents. For those who vote for me and those who don't. For all Americans."

The Democratic nominee also praised former Republicans who had denounced racism.

"Twenty years ago, when Bob Dole accepted the Republican nomination, he pointed to the exits and told any racists in the party to get out. The week after 9/11, George W. Bush went to a mosque and declared for everyone to hear that Muslims 'love America just as much as I do.' In 2008, John McCain told his own supporters they were wrong about the man he was trying to defeat. Senator McCain made sure they knew Barack Obama is an American citizen and 'a decent person.'

"We need that kind of leadership again," Clinton said.

'Taking a hate movement mainstream'

In a video published on Thursday , the Clinton campaign links clips of KKK members, including Duke, backing Trump. It also highlights Trump failing to disavow the support in an interview with CNN's Jake Tapper.

The video then cuts to media clips of Bannon joining the Trump campaign with a reporter describing the alt-right as "sort of dressed-up-in-suits version of the neo-Nazi and white supremacist movement."

Trump's campaign denounced the ad as a "disgusting new low."

"This type of rhetoric and repulsive advertising is revolting and completely beyond the pale," Trump surrogate Pastor Mark Burns said in a statement. "I call on Hillary Clinton to disavow this video and her campaign for this sickening act that has no place in our world."

Trump spokesman Jason Miller described Clinton's attacks as a "desperation play."

And Kayleigh McEnany, a Trump supporter, also told CNN's Brooke Baldwin that the real estate mogul has "repeatedly disavowed" Duke.

"What I saw was a mischaracterization of Donald Trump's record," McEnany said.

"Donald Trump has shown us who he is, and we ought to believe him. He is taking a hate movement mainstream. He's brought it into his campaign," Clinton told CNN's Anderson Cooper. "He's bringing it to our communities and our country."

Clinton added that "someone who's questioned the citizenship of the first African-American President, who has courted white supremacists, who's been sued for housing discrimination against communities of color, who's attacked a judge for his Mexican heritage and promised a mass deportation force, is someone who is very much peddling bigotry and prejudice and paranoia."

Kellyanne Conway, Donald Trump's campaign manager, rejected the idea that her candidate is the leader of the alt-right.

"We've never even discussed it internally," she said on CBS. "It certainly isn't a part of our strategy meetings. It's nothing that Mr. Trump says out on the stump."

The fact Clinton is giving her speech in Reno, a traditionally red city in a key swing state, is significant as well. Washoe County, where Reno sits, is a key county for any Republican hoping to win Nevada.

Clinton, more so than other swing states, has struggled to grow a lead in Nevada. Her campaign chalks the issues up to a smaller than average number of college educated white voters.