The candidates squared off at the University of Nevada in Las Vegas for the last time before Americans go to the polls on November 8.
Republican Mr Trump was questioned about claims he made ahead of the third debate that the election will be rigged in favour of his Democratic rival.
Asked by moderator Chris Wallace if he would accept the election result, Mr Trump replied: “I will tell you at the time. I’ll keep you in suspense.”
Mrs Clinton described Mr Trump’s remarks as “horrifying”, while the Republican National Committee said the national party would “respect the will of the people”.
“Every time Donald thinks things are not going in his direction, he claims whatever it is is rigged against him,” Mrs Clinton said.
“There was even at time when he didn’t get an Emmy for his TV programme three years in a row and he started tweeting the Emmys were rigged against him.”
In another tense exchange, Mrs Clinton branded Mr Trump a “puppet” of Russian president Vladimir Putin and challenged him to condemn Russia’s suspected involvement in the hacking of emails during the election campaign.
“I don’t know Putin,” Mr Trump said. “He said nice things about me. If we got along well, that would be good.
“He has no respect for her. He has no respect for our president.
“We’re in very serious trouble. We have a country with tremendous numbers of nuclear warheads ... 1,800 nuclear warheads and she’s playing chicken.”
Mr Clinton responded: “That’s because he’d rather have a puppet as president of the United States”.
Mr Trump replied: “No, you’re the puppet.”
The billionaire tycoon also addressed claims he sexually assaulted a number of women, accusing Mrs Clinton’s campaign team of creating the “totally false” allegations.
“I didn’t even apologise to my wife who is sitting right here because I didn’t even do anything,” he added.
“These women ... I think they either want fame or her campaign did it. And I think it’s her campaign.”
Mrs Clinton said: “Donald thinks belittling women makes him bigger. He goes after their dignity and self-worth.”
In a repeat of the bitter tone of the first two debates, Mr Trump called Mrs Clinton a “nasty woman” and claimed America would be in “some mess” if she is elected.
“The only thing you have over me is experience but it’s bad experience,” he added.
In a discussion on immigration, Mr Trump said his desire to build a wall on the US-Mexico border was to keep out “bad hombres”.
He said: “One of my first acts will be to get all of the drug lords - we have some bad, bad people in this country that have to go out ... We have some bad hombres here and we are going to get them out.”
The two candidates also clashed over the rights of women to have abortion.
Mr Trump said he planned to appoint “pro-life judges” to the Supreme Court and allow individual states to determine whether abortion should be legal.
Referring to Mrs Clinton, he said: “Based on what she’s saying ... you can take the baby and rip the baby out of the womb in the ninth month, on the final day, and that’s unacceptable.”
Mrs Clinton responded: “That’s not what happens in these cases and just using that kind of scare rhetoric is just terribly unfortunate.”
Among the debate audience was US president Barack Obama’s half brother Malik, who was a guest of Mr Trump. He had previously told the New York Post be believed the Republican “can make America great again”.