“I will tell you at the time,” he told moderator Chris Wallace. For days he has claimed the election is “rigged”.
The Las Vegas debate continued the campaign’s bitter tone, with Mr Trump calling Mrs Clinton a “nasty woman”.
Polls show Mr Trump is losing in key battleground states after facing a slew of sexual assault allegations.
The final battle of the wits came less than three weeks before election day on 8 November, when most Americans will cast their vote.
The candidates declined to shake hands before and after the political sparring, setting the tone for what would later become yet another debate marked by shouting and interrupting.
Mr Trump appealed to the Republican establishment by vowing to appoint Supreme Court justices with a “conservative bent” who would overturn a key ruling that made abortion legal in the US and protect gun rights.
He also stuck to his pledge to deport undocumented immigrants and secure US borders.
Meanwhile, Mrs Clinton firmly declared she would stand up for the LGBT community, defend abortion rights, focus on restoring the middle class and equal pay for women.
“The government has no business in the decisions that women make,” she said.
Other highlights from the debate at the University of Nevada, include:
Mrs Clinton says Mr Putin wants Mr Trump elected because he wants a puppet as US president
“You’re the puppet!” Mr Trump fired back, adding that Mr Putin had “outsmarted” and “outplayed” the former secretary of state
Mrs Clinton said Mr Trump “choked” when he met with Mexican President Enrique Pena Nieto about his plan to build the wall, but he insisted it would happen under his presidency
“We have some bad hombres and we are going to get them out,” he said
Mr Trump suggested Mrs Clinton and President Barack Obama coordinated the violence at his rally in Chicago earlier this year
When asked about her paid speech to a Brazilian bank in which she spoke of her dream of open trade and open borders, Mrs Clinton said she was talking about energy policy.
In one key exchange, he attacked her 30 years of “very bad experience” and she responded by going through her timeline, comparing where she was to where Trump was.
While she was in the Situation Room helping to take out Osama Bin Laden, “he was hosting the Celebrity Apprentice”, she said.
Donald Trump tried to be restrained. He really did. During the first section of the third presidential debate, when the topic was the Supreme Court, if you squinted you could almost imagine that this was just another presidential race, with two candidates squaring off and vigorously discussing their public policy positions on abortion and gun control.
Even the immigration discussion started reasonably civilly, until Clinton pivoted to turn a question about WikiLeaks into an attack on Donald Trump’s relationship with Russia and Vladimir Putin.
At that point, interrupting Trump returned. He called Hillary Clinton a liar and after she called him a Russian puppet, he said that was in fact her. By the time the topic turned to “fitness to be president,” the stage was set for a total meltdown. He said the women who has accused him of sexual harassment were in it for the fame and Clinton campaign stooges.
Perhaps most remarkable, however, was when moderator Chris Wallace asked Mr Trump to support the election results, no matter how they came out. He refused to do so. He accused the media of poisoning people’s minds. He said Mrs Clinton shouldn’t have been allowed to run for president. It was Mr Trump in a bunker, settling scores and lashing out at enemies real and perceived.
At that point, the headlines were written and the debate results were locked in. It was not a good night for the Republican.
Mr Trump has faced damaging fallout after a video emerged of him making obscene comments about groping women, with senior Republicans deserting him.
When pressed about sexual assault allegations made against him by several women in the wake of the video, Mr Trump said the claims had been “largely debunked”.
In addressing the groping accusations, Mrs Clinton said: “Donald thinks belittling women makes him bigger”.
“Nobody has more respect for women than I do,” Trump said as the crowd was heard scoffing.
He also blamed Mrs Clinton, whose campaign he said was responsible for drumming up the allegations.
In recent days Mr Trump has railed against the election process itself, warning the vote is “absolutely rigged” with “large-scale voter fraud” taking place.