Republican Mr Trump was questioned about his claims that the election will be rigged in favour of his Democratic rival, after he tweeted that "there was large-scale voter fraud happening on and before election day".
Asked by moderator Chris Wallace if he would accept the election result, the Republican nominee replied: "I will look at it at the time."
Mr Trump said the media was "so dishonest" and had "poisoned the minds of voters".
Of Mrs Clinton, he added: "She shouldn't be allowed to run. It's crooked. She's guilty of a very serious crime.
"Just in that respect I say it's rigged. She should never have been allowed to run for the presidency based on what she did with emails and so many other things."
Asked again if he would accept the results, Mr Trump replied: "I will tell you at the time. I'll keep you in suspense."
Mrs Clinton said Mr Trump's remarks were "horrifying".
"Every time Donald thinks things are not going in his direction, he claims whatever it is is rigged against him," she 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 even the Emmys were rigged against him.
"This is a mindset. This is how Donald thinks. It is funny but it is also really troubling - that is not the way our democracy works."
Claims v facts
Both Hillary Clinton and Donald Trump struggled in the final presidential debate to explain comments from their past. Here is a look at some of the claims.
MRS CLINTON on Mr Trump's charge that she called for open borders in a 2013 speech to a Brazilian bank: "I was talking about energy."
THE FACTS: She was actually talking about more than energy, but apparently less than an open border that immigrants can spill across at will, according to the partial transcript released by WikiLeaks.
Mrs Clinton said in the speech that "my dream is a hemispheric common market, with open trade and open borders, sometime in the future with energy that is as green as sustainable as we can get it, powering growth and opportunity for every person in the hemisphere".
The remarks suggest a broad interest in open trade but were not necessarily evidence that she would support the unfettered movement of people, as Mr Trump claimed.
MRS CLINTON: "I want to make college debt free."
THE FACTS: She might aspire to that lofty goal, but she has only proposed making college tuition free for in-state students who go to a public college or university. Even with expanded grant aid, room and board can lead students to borrow.
Mrs Clinton would have the government pay for in-state tuition at public colleges and universities for students from families earning less than 125,000 dollars a year. Students would still need to foot the bill for housing and food, which makes up more than half of the average 18,943-dollar sticker price at a four-year public university, according to the College Board.
But Mr Trump is correct that government would shoulder higher costs with Mrs Clinton's plan, which would cost the government an estimated 500 billion dollars over 10 years, with additional costs possibly for state governments.
MR TRUMP: "Her plan is going to raise taxes and even double your taxes."
THE FACTS: Mrs Clinton's plan would not raise taxes at all for 95% of Americans, according to the non-partisan Tax Policy Centre. The very wealthiest would take the greatest hit, though a doubling is highly questionable.
Two-thirds of her proposed increases would hit the top 0.1% of richest Americans, the centre estimates. The main components of her tax plan: a minimum 30% tax on those earning at least one million dollars a year, and a 5% tax surcharge for those earning more than five million a year. She would also cap the value of tax deductions and exclusions for wealthier taxpayers.
MRS CLINTON on her opposition to the Trans-Pacific Partnership trade deal: "It didn't meet my test."
THE FACTS: It met her test when she was US secretary of state and she promoted it worldwide.
Hacked emails from her campaign, released on Wednesday by WikiLeaks, showed that Jake Sullivan, her top foreign policy adviser, called her a "big champion" of the deal and worried about how to handle the issue in the face of Senator Bernie Sanders' opposition. She later flip-flopped into opposition during the Democratic primaries against Mr Sanders.
Mrs Clinton says she no longer backs the proposed trade deal as written because it does not provide enough protections for US workers on wages, jobs and the country's national security. Yet the final deal also includes some of the strongest labour protections of any US trade agreement.
MR TRUMP: "Hillary Clinton wanted the (border) wall. Hillary Clinton fought for the wall in 2006 or thereabouts. Now, she never gets anything done, so naturally it wasn't built."
THE FACTS: He is partly right. As a senator from New York, Mrs Clinton did support the 2006 Secure Fence Act, which authorised the construction of hundreds of miles of fencing along the US-Mexico border.
But it was built, contrary to Mr Trump's assertion. Nearly 700 miles of fencing was put in place during George Bush's second term and the beginning of Barack Obama's first term.
The fencing is placed largely in urban areas along the nearly 2,000-mile frontier. It is not the type of solid wall that Mr Trump has pledged to construct at Mexico's expense. The fence has miles-long gaps and gates built in to allow landowners access to their property on the south side of the fencing. Immigrants have been known to go over and around the fence.
DONALD TRUMP: Referring to a 2010 US-Russia treaty limiting both countries to 1,550 strategic nuclear warheads, Mr Trump said, "They create warheads. We can't."
The FACTS: Incorrect. The New START treaty, which Mr Trump called "Start Up", does not prevent either the US or Russia from building nuclear warheads. It restricts each country to a total of 1,550 warheads deployed on bombers, submarines and in underground silos and requires that this limit be reached by February 2018.
Mr Trump also said that after the treaty was signed, "they expanded and we didn't".
It is true that the Russians have increased the number of their deployed warheads to 1,796, and the US warhead total has dropped to 1,367. But it also is true that their total was far below that of the US when the treaty went into effect in 2010.
New data published by the State Department this month showed that although Russia has added to its warhead total, its inventory of missile launchers, such as underground silos, has shrunk.
Hans Kristensen of the Federation of American Scientists, who closely tracks US and Russian strategic forces, says the rise in Russian deployed warheads is temporary and is to be followed by the retirement of older nuclear weapons so that Moscow gets under the treaty limits. "Russian compliance with the treaty by 2018 is not in doubt," he wrote recently.
MR TRUMP: "She's lied hundreds of times to the people, to Congress, and to the FBI."
THE FACTS: His claim about the FBI does not square with what FBI director James Comey has said publicly.
At a July congressional hearing, two days after announcing that he was recommending against bringing charges against Mrs Clinton over her use of a private email server to handle sensitive information while secretary of state, Mr Comey said, "We have no basis to conclude she lied to the FBI."
MR TRUMP: Under Hillary Clinton, "six billion (dollars) went missing" at the State Department.
THE FACTS: Not quite. That figure is a distortion about a legitimate record-keeping concern. In 2014, the State Department's inspector general released an alert warning that the documentation for six billion dollars in State Department contracts was incomplete. But there is no reason to think that all occurred under Mrs Clinton. The inspector general, Steve Linnick, specifically disavowed the conclusion that the money went missing.
MR TRUMP: "President Obama has moved millions of people out ... millions of people have been moved out of this country."
THE FACTS: True. Mr Obama has overseen the deportation of more than 2.5 million immigrants since taking office in January 2009.
During Mr Obama's first term hundreds of thousands of immigrants were deported annually, following a trend of increasing deportations started under George Bush. The administration set a record in 2014 when more than 409,000 people were sent home.
During his second term, deportations have steadily declined as he has opted to focus immigration enforcement resources on finding and deporting serious criminals and those who pose a threat to national security or public safety.
But Mr Trump also claims that "nobody knows about it, nobody talks about it" and that is far from the truth. Mr Obama has been dubbed "the deporter in chief" by immigration advocates and opponents of his immigration enforcement policies.
MRS CLINTON: "I disagreed with the way the court applied the Second Amendment" in the District of Columbia vs Heller decision in 2008. "I was upset because unfortunately dozens of toddlers injure themselves and even kill people with guns ... But there's no doubt I respect the Second Amendment, that I believe there's an individual right to bear arms."
THE FACTS: While Mrs Clinton emphasised the protection of children from gun accidents, the main holding in that case was far broader: that individuals have a right to own guns, at least in their homes and for self-defence. The case marked the first time the court said that individuals have a Second Amendment right to own a gun.
The decision struck down Washington's ban on handgun ownership as well as a separate requirement that people who have other guns store them either with trigger locks or disassembled. The court said both provisions violated the Second Amendment.