In a remarkable statement that seemed to cast doubt on American democracy, Donald J. Trump said Wednesday that he might not accept the results of next month’s election if he felt it was rigged against him — a stand that Hillary Clinton blasted as “horrifying” at their final and caustic debate on Wednesday, reports the New York Times.

The debate was won by Clinton with 52% as against Trump’s 39% but it was a vitriolic debate interjected with curses, abuses from both candidates and even name-calling.

Mr. Trump, under enormous pressure to halt Mrs. Clinton’s steady rise in opinion polls, came across as repeatedly frustrated as he tried to rally conservative voters with hard-line stands on illegal immigration and abortion rights. But he kept finding himself drawn onto perilous political territory by Mrs. Clinton and the debate’s moderator, Chris Wallace.

He sputtered when Mrs. Clinton charged that he would be “a puppet” of President Vladimir V. Putin of Russia if elected. He lashed out repeatedly, saying that “she’s been proven to be a liar on so many different ways” and that “she’s guilty of a very, very serious crime” over her State Department email practices. And by the end of the debate, when Mrs. Clinton needled him over Social Security, Mr. Trump snapped and said, “Such a nasty woman.”

Mrs. Clinton was rarely rattled, and made a determined effort to rise above Mr. Trump’s taunts while making overtures to undecided voters. She particularly sought to appeal to Republicans and independents who have doubts about Mr. Trump, arguing that she was not an opponent of the Second Amendment as her opponent claimed, and promising to be tougher and shrewder on national security than Mr. Trump.

But it was Mr. Trump’s remark about the election results that stood out, even in a race that has been full of astonishing moments.

Mr. Trump insisted, as he has in recent days, that the general election has been rigged against him, and he twice refused to say that he would accept its result.

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“I will look at it at the time,” Mr. Trump said. “I will keep you in suspense.”

“That’s horrifying,” Mrs. Clinton replied. “I am appalled that someone who is the nominee of one of our two major parties would take that position.”

Mrs. Clinton then ticked off the number of times he had deemed a system rigged when he suffered a setback, noting he had even called the Emmy Awards fixed when his show, “The Apprentice,’’ was passed over.

“It’s funny, but it’s also really troubling,” she said. “That is not the way our democracy works.”

With 20 days left before Election Day and early voting already underway in Florida, Ohio and several other key states, the debate felt less like an argument between equals than a last-ditch attempt by a fading candidate, Mr. Trump, to save himself.

Mr. Trump sought throughout the debate to recover from a politically damaging three weeks. He has been unable to gain traction in the polls from his strategy of assailing the Clintons as corrupt and immoral; the news media as biased and bent on rigging the election against him; and the nine women who have come forward to accuse him of unwanted sexual advances as liars and, in some cases, unattractive.

Mr. Trump said, in response to a question from the debate moderator, Chris Wallace of Fox News, that the claims of the women had been “debunked” and that they had been put forward by Mrs. Clinton’s campaign.

Fact Checks of the Third Presidential Debate

Reporters for The New York Times fact-checked the statements made by Hillary Clinton and Donald J. Trump during Wednesday’s presidential debate.

But after he denied ridiculing the looks of the women accusing him of sexual harassment — “I did not say that,” he repeated three times — Mrs. Clinton repeated nearly verbatim his two comments from last week about the appearances of a pair of his accusers.

“Donald thinks belittling women makes him bigger,” she said. “He goes after their dignity, their self-worth; there’s not a women anywhere who doesn’t know what that feels like.”

After Mrs. Clinton finished an extended condemnation, Mr. Trump said only: “Nobody has more respect for women than I do, nobody.”

In contrast to their two previous debates, the 90-minute discussion covered significant substantive ground. On immigration, Mr. Trump argued that Mrs. Clinton wanted to give illegal immigrants “amnesty” and that “she wants to have open borders.”

“We have to have strong borders, we have to keep the drugs out of our country — right now we’re getting the drugs, they’re getting the cash,” he added. “We have some bad hombres here, and we’re going to get them out.”

Mrs. Clinton recalled meeting a young girl in Las Vegas whose parents had been threatened, and noted that Mr. Trump has said that every illegal immigrant would ultimately be subject to deportation.

“I don’t want to rip families apart,” Mrs. Clinton said. “I don’t want to see the deportation force that Donald has talked about in action in our country.” She added that Mr. Trump’s focus on deportation would “rip our country apart.”

At several points, Mrs. Clinton tried to bait Mr. Trump into an outburst, such as when she said that he “choked” during his meeting this summer with the president of Mexico when he did not press him on Mexico paying to build a border wall.

But Mr. Trump pivoted to attack former President Bill Clinton’s administration for supporting the North American Free Trade Agreement and assailed Mrs. Clinton for her past comments supporting “open borders” in the Western Hemisphere.

The two candidates also tangled over abortion rights. After initially declining to flatly say whether he would support overturning Roe v. Wade, the 1973 Supreme Court decision that legalized abortion, Mr. Trump conceded that the justices he would appoint to the court would do just that.

“If we put another two or perhaps three justices on, that’s really what will happen,” he said. “That’ll happen automatically in my opinion.”

Mrs. Clinton responded with a full-throated defense of Roe and abortion rights.

“The government has no business in the decisions that women make,” she said.