Here are key moments from the fiery town-hall style presidential debate between Republican Donald Trump and Democrat Hillary Clinton at Washington University in St. Louis on Oct. 9. (Sarah Parnass/The Washington Post)

The second presidential debate veered into ugly territory Sunday night in St. Louis, as the two nominees swapped insults and interruptions.

Republican Donald Trump at one point said that his rival Hillary Clinton had “hate in her heart,” and showed it by saying that half of his supporters were in the “basket of deplorables.”

Clinton in turn accused Trump of living in an “alternate reality” and of peddling what she called the “racist lie” that President Obama was not born in the United States.

That exchange came as an especially bitter, boundary-breaking debate neared its conclusion.

Republican presidential nominee Donald Trump told Hillary Clinton that if he becomes president, he will instruct the attorney general to hire a special prosecutor to investigate her. (The Washington Post)

The words “sex tape” even made their debut in the solemn tradition of American presidential debates on Sunday night, as Trump denied doing something he had actually done: asking his Twitter followers to “check out sex tape” of a former Miss Universe with whom he was feuding.

“It wasn’t, ‘Check out a sex tape,’ ” Trump said, saying instead that he wanted followers to examine the life of Alicia Machado, the former Miss Universe. Clinton had brought her up in the previous debate, talking about a 1990s episode when Trump made a public spectacle of Machado’s weight gain.

Trump’s message, sent out on Twitter on Sept. 30, was this: “Did Crooked Hillary help disgusting (check out sex tape and past) Alicia M become a U.S. citizen so she could use her in the debate?”

The evening’s most genteel moments came in the very last minutes, when a questioner asked the two to say something nice about one another. Clinton said she respected Trump’s children, but then quickly pivoted to talk about herself, using the night’s last seconds of airtime to run through her campaign résumé.

Trump, who had been on the attack all night, reacted to the same question with a direct, and seemingly sincere, moment of praise for Clinton herself.

“She doesn’t quit. She doesn’t give up. I respect that. I tell it like it is. She’s a fighter,” Trump said. “I consider that to be a very good trait.”

One of the night’s most striking moments came when Trump contradicted his running mate, Indiana Gov. Mike Pence, on a question of American policy in Syria.

During the second presidential debate on Oct. 9, Republican presidential nominee Donald Trump accused former president Bill Clinton of abusing women. (The Washington Post)

During the vice-presidential debate on Tuesday, Pence was asked what the United States should do to protect rebels and civilians in the city of Aleppo, which is under heavy bombardment by Syrian government forces and their Russian allies.

Pence called for a strong reaction: “The United States of America should be prepared to use military force to strike military targets of the Assad regime to prevent them from this humanitarian crisis that is taking place in Aleppo.”

Such a move could provoke a dangerous crisis with the Russian government, which Trump has said the United States should seek a better relationship with.

Trump was asked whether he agreed. In one of the most direct answers he gave all night, Trump said Pence was wrong.

“He and I haven’t spoken. And I disagree,” Trump said.

“Right now, Syria is fighting ISIS,” Trump said, referring to the Islamic State. Outside experts have criticized Russia and Syria for focusing on other rebel groups, instead of focusing on the Islamic State. “I believe we have to get ISIS. We have to worry about ISIS before we get too much involved” with the Syrian regime, Trump said.

Trump was then asked about how to prevent the fall of Aleppo.

Pence, after all, had been willing to risk a military conflict with Russia to prevent its fall. Trump said, in essence, that this outcome was inevitable.

He said Aleppo “basically has fallen.”

At another moment, Trump seemed to concede that he had avoided paying any federal income taxes for some recent years by taking advantage of tax loopholes and a massive $916 million loss he reported in 1995.

“Of course I do. Of course I do,” Trump said when moderator Anderson Cooper asked whether he’d used that loss — first reported by the New York Times — to erase all his federal income tax liabilities. “And so do all of her donors,” he said, referring to Clinton.

Trump provided no details about how many years he had avoided paying income taxes but affirmed again that he had. “I absolutely used it,” he said, when Cooper asked. Trump also repeated an argument he had made on the campaign trail, that his skillful use of loopholes in the tax code made him the best qualified to eliminate those loopholes. “I understand the tax code better than anybody that’s ever run for president,” he said, and he argued that Clinton could not fix the system because of Wall Street donors and because she had failed to reform the system during her years as a senator and first lady.

Clinton, in her response, argued that Trump would only cement an unfair system in place: “Donald always takes care of Donald, and people like Donald,” she said.

The second presidential debate was unusually bitter, with the two candidates taking steps unheard-of in the genteel tradition of debates — which, typically, are the kind of discussions where “There you go again” is considered a flaming zinger.

In this debate, the two interrupted each other often. Trump referred to Clinton as “the Devil’ and promised that if elected he would order the Justice Department to reinvestigate her for her use of a private email server to handle government business while secretary of state. Clinton said at one point that Trump lives “in an alternate reality.”

The debate topics ranged from news of the past week as well as stances taken by the candidates over the previous year.

Trump said his proposal to ban foreign Muslims from entering the United States has “morphed,” but the Republican nominee declined to give details about what it had morphed into.

“The Muslim ban is something that, in some form, has morphed into an extreme vetting from certain areas of the world,” Trump said, when asked whether he had backed off the position.

Moderator Martha Raddatz sought to gain clarification, interrupting Trump at several points to ask what his position was. “Would you please explain whether or not the Muslim ban still stands?”

“It’s called extreme vetting,” Trump said, but he did not say much more about how the vetting process would work — or how it would be different from the current methods used to screen immigrants and refugees for terrorist affiliations.

Trump also asserted, once again, that he had opposed the war in Iraq before it began. That is incorrect. In fact, Trump was asked on Sept. 11, 2002 — before the invasion — if he supported the war.

“Yeah, I guess so. You know, I wish the first time it was done correctly,” Trump told interviewer Howard Stern during a radio interview, referring the 1991 Persian Gulf War.

“It’s been debunked,” Clinton said, about Trump’s claim to have opposed the war.

“I was against the war in Iraq, and it hasn’t been debunked,” Trump said.

Earlier, in an unprecedented threat during a presidential debate, Trump promised that — if he was elected — he would instruct the Justice Department to investigate his rival.

“I didn’t think I’d say this, but I’m going to say this, and I hate to say it, but if I win, I am going to instruct my attorney general to get a special prosecutor to look into your situation,” Trump said. “There’s never been anything like it. And we’re going to get a special prosecutor.”

Trump seemed to be speaking about Clinton’s use of a personal email server to handle government business while she was secretary of state. That has already been the subject of an FBI inquiry, which ended with FBI Director James B. Comey calling Clinton and her staff “extremely careless” but recommending no criminal charges.

His promise to use his executive power to reopen that case, and have it investigated again, was unlike anything in recent presidential debates.

“It’s just awfully good that someone with the temperament of Donald Trump is not in charge of the law in our country,” Clinton said.

“Because you’d be in jail,” Trump said.

The first half-hour of this debate was dominated not by questions from the undecided voters in the audience, but by interruptions and accusations by Trump himself. At one point, Trump referred to the endorsement by Sen. Bernie Sanders (Vt.) of Clinton as a deal with “the Devil.”

The debate opened with a question as to whether the campaigns were setting a good example for the nation’s youth, but it quickly turned to a discussion about a recent revelation of a damaging video for Trump.

The Republican nominee rejected a question that called his remarks about groping women – captured in a 2005 video – “sexual assault,” during the second presidential debate on Sunday night.

“That is sexual assault. You bragged that you committed sexual assault,” moderator Anderson Cooper said, and then asked Trump whether he understood the implications of what he said.

“I didn’t say that at all. I don’t think you understood what was said. This was locker-room talk,” Trump said. “Certainly I’m not proud of it. But this is locker-room talk.”

Cooper kept on, asking Trump whether he had actually committed the acts he alluded to in the video – which included kissing women without their consent, and groping women’s genitals. Trump repeatedly sought to turn the subject to other subjects, including in some cases with seeming non-sequitur.

“I’m very embarrassed by it. I hate it. It’s locker-room talk,” Trump said at one point. “I will knock the hell out of ISIS.”

Clinton, in her response, said that she considered Trump different from past Republican nominees.

“I never questioned their fitness to serve. Donald Trump is different,” she said. “What we all saw and heard on Friday was Donald talking about women, what he thinks about women, what he does to women, and he has said that the video doesn’t represent who he is. . . . It represents exactly who he is.”

The night’s dark tone was presaged by a news conference Trump held about 90 minutes before the debate began at Washington University in St. Louis. Trump was joined by four women, all of whom said they had been mistreated by Hillary Clinton or former president Bill Clinton. One of the women was Paula Jones, who had accused Bill Clinton of sexual harassment in the early 1990s. Another was Juanita Broaddrick, who at the news conference said Bill Clinton had raped her in 1978.

“Mr. Trump may have said some bad words,” Broaddrick said. “But Bill Clinton raped me and Hillary Clinton threatened me. I don’t think there’s any comparison.”

Broaddrick has made such statements before, but it has never been criminally litigated, and the Clintons deny the accusations.

As Trump began and ended the news conference, reporters shouted questions related to the 2005 video. ““Mr. Trump does your star power allow you to touch women without their consent?” a reporter asked. Trump ignored the questions, then left.

For Trump, the stakes for this debate would have been high in any event: He had seen his poll numbers slide after a weak and rambling performance during the first debate in late September.

Now, however, Trump is in worse shape — and in far greater need of a surprising, campaign-changing performance. That’s due to the release of the 2005, video, first published by The Washington Post. It set off a cascade of criticism from Trump’s fellow Republicans and led dozens of them to formally renounce the party’s nominee.

Trump’s supporters said they were hoping to see a humble, focused performance, in which he could seem contrite about the 2005 remarks, and then move on.

“He has to reach inside himself and realize what he’s capable of doing. He has to live it out, and it’s going to be a uniquely personal moment. No one else can figure it out,” said former House speaker Newt Gingrich (R-Ga.).

On Sunday, however, Trump was showing no sign of a contrite approach. Instead, in interviews and social media posts, Trump made clear that he has no plans to back down — and that he intends to criticize Clinton for her treatment of women who over the years have accused her husband of unwanted sexual advances.

Trump also seemed to blast his fellow Republicans, scorning them for leaving him at this moment.

“So many self-righteous hypocrites. Watch their poll numbers — and elections — go down!” read one Trump tweet Sunday.

“Tremendous support (except for some Republican “leadership”). Thank you,” another read.

Dozens of elected officials, including Sen. John McCain (R-Ariz.), said Saturday that they could no longer support Trump. A growing chorus called for him to drop out of the race. Even his running mate, Pence, said he could not defend Trump’s remarks. Trump was scheduled to campaign with House Speaker Paul D. Ryan on Saturday in Wisconsin, but Ryan asked the nominee not to attend. Pence was scheduled as a stand-in, but he, too, decided to stay away. Although Ryan criticized Trump’s remarks, he has not withdrawn his support for the candidate.

As Trump jetted to St. Louis, Sen. Jeff Sessions (R-Ala.) was on the campus of debate host Washington University on Sunday afternoon with his phone to his ear urging fellow congressional Republicans to settle down and stick with the party’s standard-bearer.

“He’s charged up,” Sessions said of Trump in an interview with The Post. “I believe he can turn this around. I think our party leaders need to slow down and give him a chance to make his case.”

Robert Costa, Jose A. DelReal, Abby Phillip and John Wagner in St. Louis; Anne Gearan in Washington; and Mike DeBonis in Chicago contributed to this report.