Presidential Debate Fact-Check: What Donald Trump and Hillary Clinton Are Claiming Some of the key exchanges fact-checked in the final presidential debate.

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The third and final presidential debate between Hillary Clinton and Donald Trump, in Las Vegas, started out as a policy discussion but quickly turned tense, with both candidates accusing the other of lying or making misleading statements about their records and past positions.

The showdown came as Trump’s campaign has been consumed by allegations of sexual misconduct — all of which he has vehemently denied — and Clinton is grappling with the fallout from the publication of her campaign chairman’s email archives by WikiLeaks.

Debate moderator Chris Wallace of Fox News attempted to focus on six topics: debt and entitlements, immigration, the economy, the Supreme Court, foreign hot spots and fitness to be president.

ABC News fact-checked some of the most noteworthy claims made in the debate:

Fact-check No. 1: Clinton said 17 intelligence agencies "confirmed" Russia is trying to influence our election.

Clinton: Russians "have hacked American websites, American accounts of private people, of institutions, then they have given that information to WikiLeaks for the purpose of putting it on the internet. This has come from the highest levels of the Russian government, clearly from Putin himself, in an effort, as 17 of our intelligence agencies have confirmed, to influence our election. So I actually think the most important question of this evening, Chris, is finally will Donald Trump admit and condemn that the Russians are doing this?"

Our grade: True

Explanation: The head of the U.S. intelligence community, overseeing 17 intelligence-related organizations, has said publicly that the community is "confident that the Russian government directed" the recent hacks in an attempt "to interfere with the U.S. election process."

Fact-check No. 2: Trump said thousands of Syrians are coming to the United States and there is no way to determine where they came from.

Trump: "He has thousands and thousands of people. They have no idea where they come from, and you see, we are going to stop radical Islamic terrorism in this country."

Our grade: False

Explanation: This claim that the U.S. is unable to accurately identify Syrian refugees is categorically denied by the State Department and the multiple U.S. government agencies tasked with vetting refugees. The State Department has said, “Applicants to the U.S. refugee admissions program are currently subject to the highest level of security checks of any category of traveler to the United States.”

Fact-check No. 3: Clinton claims Trump is willing to break up NATO.

Clinton: "That the Russians have engaged in cyberattacks against the United States of America, that you encouraged espionage against our people, that you are willing to spout the Putin line, sign up for his wish list, break up NATO, do whatever he wants to do and that you continue to get help from him because he has a very clear favorite in this race. So I think that this is such an unprecedented situation. We've never had a foreign government trying to interfere in our election."

Our grade: True

Explanation: Trump drew international headlines when he said he would be willing to have the U.S. leave NATO.

For example, on April 27, Trump said, "In NATO, for instance, only four of 28 other member countries besides America are spending the minimum required 2 percent of GDP on defense. We have spent trillions of dollars over time on planes, missiles, ships, equipment, building up our military to provide a strong defense for Europe and Asia. The countries we are defending must pay for the cost of this defense, and if not, the U.S. must be prepared to let these countries defend themselves. We have no choice."

Fact-check No. 4: Trump claims that he is endorsed by Immigration and Customs Enforcement (ICE) and Customs and Border Protection (CBP) and that the agencies support building a border wall.

Trump: "Hillary wants to give amnesty. She wants to have open borders. As you know, the Border Patrol agency, 16,500, plus ICE last week endorsed me. First time they've ever endorsed a candidate. It means their job is tougher, but they know what's going on. They know it better than anybody. They want strong borders. They feel we have to have strong borders."

Our grade: Mostly false

Explanation: ICE and the CBP are barred from making political endorsements.

"Per the Hatch Act, federal agencies are prohibited from engaging in partisan political activity, including the endorsement of any candidate for office. U.S. Immigration and Customs Enforcement has not and will not endorse any candidate for office," said an ICE representative.

Trump has repeatedly said the agency endorsed him. However, he did receive endorsements from unions representing ICE and CBP employees.

In April the head of ICE, Sarah Saldana, told lawmakers that completely sealing the southwestern border would not be effective and would not protect the United States. "[A wall] doesn't sound like it would secure anything, actually," she said.

Fact-check No. 5: Trump claims Clinton is responsible for a nuclear weapons agreement that favors Russia.

Trump: "Let me tell you. Putin has outsmarted her and Obama at every single step of the way. Whether it's Syria, you name it, missiles. Take a look at the START-Up that they signed. The Russians have said, according to many, many reports, I can't believe they allowed us to do this. They create warheads, and we can't. The Russians can't believe it. She has been outsmarted by Putin.”

Our grade: Mostly true

Explanation: Trump alleges that New START allows Russia but not the United States to build warheads. He appears to call the treaty “START-Up.”

Trump is referring to the 2011 New START (Strategic Arms Reduction Treaty) nuclear weapons agreement between the United States and Russia — which was negotiated while Clinton was secretary of state. The treaty limits to 1,550 the number of deployed nuclear warheads, not the number of nuclear warheads in either country’s nuclear stockpile, which may be higher. "Deployed" means the warheads are deployed on ICBMs, submarines or heavy bombers.

The treaty did not require the destruction of nuclear weapons or the reduction of nuclear stockpiles. When the agreement was ratified, Russia was under the cap at 1,537 warheads, while the United States was over the cap at 1,800. By March 2016, Russia had increased the number of deployed warheads to 1,735. The number of warheads deployed by the United States has decreased to 1,481.

The Russian increase has been attributed to a temporary situation as Russia replaces warheads built decades ago with newer ones.

The United Stated and Russia have until Feb. 5, 2018, to meet the New START’s reduction in deployed warheads.

Fact-check No. 6: Clinton claims that Trump wants Japan, South Korea and Saudi Arabia to have nuclear weapons.

Clinton: "He’s advocated more countries getting them — Japan, Korea, even Saudi Arabia."

Our grade: Yes and no

Explanation: Trump has said that U.S. allies should pay more of their defense costs and take more responsibility for their own protection. Earlier this year, he seemed to say that Japan might be better off if it had nuclear weapons to defend itself from North Korea. At a town hall in April, he also seemed to support Saudi Arabia's having nuclear weapons but quickly reversed himself. In June he denied that he wanted Japan to get nuclear weapons. He wants U.S. allies to pay more for their defense and has at times indicated it would be all right for Japan to have access to nuclear weapons to defend itself from North Korea.

Fact-check No. 7: Trump says Clinton’s economic plan is going to raise taxes, possibly doubling rates.

Trump: "Well, first of all, before I start on my plan, her plan is going to raise taxes and even double your taxes. Her tax plan is a disaster. And she can say all she wants about college tuition — and I'm a big proponent, we're going to do a lot of things for college tuition — but the rest of the public's going be paying for it. We'll have a massive, massive tax increase under Hillary Clinton's plan."

Our grade: Mostly false

Explanation: Clinton has proposed raising taxes on high earners, but none of the proposals she has outlined would double taxes on any Americans. According to Kyle Pomerleau of the Tax Foundation, Clinton would raise taxes overall, but her changes to the tax code would mostly burden high-income taxpayers.

Fact-check No. 8: Trump says health care premiums will rise next year by more than 100 percent.

Trump: "But 'Obamacare' has to go. It's — the premiums are going up 60, 70, 80 percent. Next year they're going to go up over 100 percent."

Our grade: Mostly false

Explanation: Health care costs have been on the rise in a number of categories — health insurance premiums, out-of-pocket costs, employer costs to insure employees, to name a few. However, according to the Department of Health and Human Services, the costs that matter to individuals do not appear to approach this percentage, at least not in a single year. According to the HHS report, the average premium under the Affordable Care Act for 2016 plans rose to $408 per month, which is about a 9 percent increase from last year.

Fact-check No. 9: Trump claims Clinton wanted a border wall.

Trump: "Hillary Clinton wanted the wall. Hillary Clinton fought for the wall in 2006 or thereabouts. Now, she never gets anything done, so naturally the wall wasn't built. But Hillary Clinton wanted the wall."

Our grade: Yes and no

Explanation: Clinton voted for a bill in 2008 calling for a barrier fence along the southern U.S. border but refers to it as a fence, not a wall. Clinton has pointed to this vote herself and cited her desire for border security. Last November while campaigning, she said, "I voted numerous times when I was a senator to spend money to build a barrier to try to prevent illegal immigrants from coming in ... And I do think you have to control your borders."

But Clinton refers to her vote as supporting a fence — as it was termed in the bill's name and accompanying fact sheet — not a wall, which Trump has called for multiple times. A fragmented fencing system already exists along the southern U.S. border.

Fact-check No. 10: Trump claims the Clinton State Department lost $6 billion.

Trump: "The problem is you talk but you don't get anything done, Hillary. You don't, just like when you ran the State Department — $6 billion was missing. How do you miss $6 billion? You ran the State Department. Six billion dollars was either stolen — they don't know, it's gone. Six billion dollars. If you become president, this country is going to be in some mess, believe me."

Our grade: False

Explanation: The claim appears to come from a 2014 alert issued by the State Department’s inspector general that said $6 billion in Iraq contracts were incomplete or could not be located. It did not say $6 billion had been lost.

The alert said that over the past six years, the watchdog for the Department of State "contracts with a total value of more than $6 billion in which contract files were incomplete or could not be located at all." But after subsequent media reports suggested that the State Department had lost the money, Inspector General Steve Linick wrote a letter published in The Washington Post saying that claim was false. "Some have concluded based on this that $6 billion is missing," he wrote on April 13, 2014. "The alert, however, did not draw that conclusion. Instead, it found that the failure to adequately maintain contract files — documents necessary to ensure the full accounting of U.S. tax dollars — 'creates significant financial risk and demonstrates a lack of internal control over the department's contract actions." An analysis by the Post states that because the contracts in question were issued from October 2004 to October 2011, "it’s safe to assume that more than half of the contracts were issued before Clinton took charge of the State Department."

Fact-check No. 11: Trump says ISIS is in 32 countries.

Trump: "And what happened is now ISIS is in 32 countries. And now I listen how she is going to get rid of ISIS. She is going to get rid of nobody."

Our grade: False

Explanation: The 32 number is higher than any reliable source has estimated.

A terrorist threat snapshot issued by the House Homeland Security Committee this month read, "ISIS, its affiliates and supporting groups have operated in approximately two dozen countries or territories, including Afghanistan, Algeria, Bangladesh, Brazil, Egypt, India, Indonesia, Iraq, Jordan, Libya, Lebanon, Nigeria, the Palestinian territories (Gaza), Pakistan, Philippines, Russia (North Caucus region), Sudan, Syria, Tunisia and Yemen." A report by the nonpartisan Congressional Research Service in late June concluded that in addition to Iraq and Syria (where most of the group is), ISIS has "affiliates in several other countries." The terrorism snapshot did say that at least 34 Islamic extremist groups have pledged allegiance to ISIS, but one senior ISIS expert at the State Department told ABC News that's not the same thing. The expert said there are only a few countries where the group has sent operatives and resources. "It's not like there's an inkblot of ISIL spreading all over the world in the last two years," the official said. "If you had a pre-ISIL map showing where terrorist networks operated around the world and a map today showing where ISIL claims affiliates, the marks on the map would actually show very little change."

Fact-check No. 12: Trump says Mosul fell to ISIS because of a troop withdrawal agreement.

Trump: "Let me tell you, Mosul is so sad. We had Mosul. But when she left, when she took everybody out, we lost Mosul. Now we're fighting again to get Mosul."

Our grade: Yes and no

Explanation: Referring to the ongoing Iraqi offensive to retake Mosul from ISIS, Trump implies the city was lost to ISIS in 2014 because of a security vacuum created by the withdrawal of American troops from Iraq in 2011. The 2008 Status of Forces Agreement, which set a timetable for all American troops to leave Iraq by the end of 2011, was negotiated by the administration of George W. Bush. President Barack Obama and then–Secretary of State Clinton favored keeping some American troops in Iraq beyond that date. But after Iraq was not willing to provide immunity guarantees for U.S. troops, Obama ordered that the withdrawal continue as scheduled. It is unclear whether keeping several thousand American troops as trainers in Iraq could have prevented the rise of ISIS.

Fact-check No. 13: Trump says Clinton wants open borders.

Trump: "Well, first of all, she wants to give amnesty, which is a disaster and very unfair to all the people that are waiting in line for many years. We need strong borders. In the audience tonight we have four mothers of — I mean, these are unbelievable people that I've gotten to know over a period of years whose children have been killed, brutally killed by people that came into the country illegally. You have thousands of mothers and fathers and relatives all over the country. They're coming in illegally. Drugs are pouring in through the border. We have no country if we have no border. Hillary wants to give amnesty. She wants to have open borders."

Our grade: Yes and no

Explanation: According to emails released by WikiLeaks, Clinton gave remarks in 2013 in which she said, "My dream is a hemispheric common market, with open trade and open borders, sometime in the future, with energy that is as green and sustainable as we can get it, powering growth and opportunity for every person in the hemisphere."

Clinton says she was talking about energy, not immigration, and her immigration plan does not call for open borders or amnesty. Her immigration plan, similar to what Obama is currently doing, does call for border enforcement, but the resources would be focused on "detaining and deporting those individuals who pose a violent threat to public safety," according to her website.

Fact-check No. 14: Clinton claims her tax plan wouldn't add to the national debt.

Clinton: "What I have put forward doesn't add a penny to the debt."

Our grade: False

Explanation: Clinton claims her tax plan won't increase the national debt, but the nonpartisan Committee for a Responsible Federal Budget estimates that her economic plan would increase the debt by $200 billion over a decade.

Regardless of which candidate is elected to the White House, the national debt, which is now more than $14 trillion, is likely to grow by about $9 trillion over the next 10 years, according to the Committee for a Responsible Budget.

ABC News' Margaret Chadbourn, Serena Marshall, Jordyn Phelps, Audrey Taylor, Geneva Sands, Lauren Pearle, Erin Dooley, Mike Levine, Luis Martinez, Justin Fishel, Ely Brown, Zunaira Zaki, Dan Childs and Kate Shaw contributed to this report.