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This is a rush transcript from "On the Record," June 17, 2016. This copy may not be in its final form and may be updated.


GRETA VAN SUSTEREN, FOX NEWS HOST: Welcome to an ON THE RECORD special "Terror in America: ISIS" and Election 2016."

From the campaign trail to the debate stage, hot button issues like a Muslim ban to taking in refugees to closing the border have taken over this campaign season. And just this week, the vicious Orlando massacre thrusting terror into the forefront of this 2016 campaign.

Donald Trump and Secretary Hillary Clinton have wildly different approaches. And tonight we investigate both candidates and how each says he or she will destroy ISIS. Americans are scared. And candidates' proposed strategies could swing the entire election.

So we begin with former New York City Mayor Rudy Giuliani.

Good evening, mayor.

RUDY GIULIANI, FORMER NEW YORK CITY MAYOR: Good evening, Greta. Nice to talk to you.

VAN SUSTEREN: Mayor, this past week, it has been just awful in Orlando. But it is certainly no surprise.

In 2014, in January, President Obama said that ISIS was JV. Two and a half years later, it has now metastasized all over the globe.

Tell me, going into November, this election, tell me how a President Trump would differ in terms of handling this ISIS and what you predict a president Hillary Clinton would do?

GIULIANI: Well, I mean, you couldn't have done worse than Hillary Clinton and Barack Obama. I mean, if I were Donald, I would use that as my campaign slogan.

I can't do worse than what they did. I mean, the reality is four or five years ago, there was an ISIS, but it wasn't the organization it is today. When he said it was the JV, he was really talking about the ISIS of two or three years ago and the ISIS that he kind of inherited.

He is the one that made it into a varsity Islamic terrorist organization by number of things, not intervening in Syria when he should have five years ago.

John McCain and Lindsey Graham are absolutely right. He, by doing that, made it possible for ISIS to metastasize. I mean, they were a cancer already, but they metastasized under a failed Hillary Clinton, Barack Obama policy.

Then his 12 threats to Assad and his failure to take action after those 12 threats lost all credibility for the United States. And I know Islamic terrorism since 1973, Greta, so I know what I'm talking about. And I have read most of their major works.

And the only thing you can do to stop Islamic extremist terrorism is you have to be on offense. If you are on defense, as we have been in the last three or four years, or as we were before September 11th, when we took the hit at the coal and didn't strike back, and we were hitting East Africa and struck back but very meekly, when you do that, you invite the kind of attacks we are getting now.

And I don't know if you realize it, but they really are beginning to expand exponentially. We've had four massive attacks in less than a year. Right?

Santa Barbara, Brussels, Paris, and now this tragedy in -- horrible attack.

VAN SUSTEREN: But it's even more than that. In the Philippines this week, an ISIS affiliate beheaded a Canadian, Boko Haram in Africa, they are an ISIS affiliate.

GIULIANI: And in France. The police officer and his wife with a knife. And people are talking about gun control.

I mean, so if they don't have a gun, they use a knife. They don't have a knife, they use a bomb. They don't have a bomb, they use anthrax. They are not using anthrax, they are going to use dirty bombs.

When Iran starts to make nuclear material available to them, if Iran isn't already making nuclear material available to them.

So, I mean, the reality is that weakness in the face of this kind of insane religious ideology only breeds more attack.

And all Barack Obama and Hillary Clinton have been from the day they started is weak. Taking all of our troops out of Iraq, taking all of our troops out of Afghanistan, leaving nothing behind, of course you aren't going to find out about the development of ISIS. There was nobody there to tell you about it.

I mean, you have to be dumb not to figure out why this was a terrible mistake. So, what would a President Trump do?

Here's what I would advise him to do. Number one, he's absolutely right. You've got to face your enemy and call them what they are. It's Islamic extremist terrorism.

That is the philosophy behind the attack that went on in Orlando. And in this particular case, it was focused against a group of people that are considered enemies of fundamentalists extremist Muslims, gay and lesbian people.

I mean, we have seen them throw homosexual men off buildings. They have sent us pictures of it just to show us how much they hate people that are gay and lesbian.

So that adds an extra dimension to it. But this is very similar to when they take a group of Christians and chop their heads off. If you are a Christian, you are infidel. If you are a gay and a lesbian, you are infidel. If you are a Jew, you are infidel. If you are not, they are kind of fundamentalist Muslim, and in Muslim, you are an infidel and they will chop your head off.

And then you've got to put boots on the ground. I don't want to hear ever again, no boots on the ground. I don't want to hear that.

VAN SUSTEREN: He talks about two things that I hear. Number one, he talks about a ban on Muslims, which look, you know, there are Muslims serving in our military who are very fine men and women, and loyal Americans.

Then he talks about a wall, but look at the vicious killer in Orlando. He got his inspiration over the internet. The internet isn't blocked by a wall.

GIULIANI: The ban should be a ban on Muslims coming from countries in which there are serious threats to the United States. And those people should only be allowed in, if at all, if there is a vetting process that the director of the FBI is comfortable with. And James Comey says he is not comfortable with the vetting process for people coming in from particularly Syria, in this particular case.

But, mainly, you are asking me about ISIS. The approach to ISIS has to be recognized who they are and what they are. And we have to commit, not just bombings, but we have to commit troops to wiping them out. We should have done it five years ago. We need to create a no-fly zone in Syria.

We've got to push Assad back and we have to take those refugees and put them in Syria with a no-fly zone protected by the American Air Force, the American military and everybody else who wants to join us.

Look, the president of France was willing to do this two or three years ago. I was so embarrassed when the president of France wanted to take a more aggressive position with regard to Islamic extremist terrorism than the president.

The president of France uses the words Islamic extremist terrorism. In fact, when the foreign minister of France used those words, the White House took it out of the tape. So we have something absurd going on here.

You couldn't do worse than the policies of Hillary Clinton and Barack Obama. And what we aid is a president who is going to commit himself to wiping out ISIS. No timetable. Like the stupidity of the timetable we had in Iraq and Afghanistan. What war was ever fought on a timetable? Here is the timetable, when they stop threatening us.

VAN SUSTEREN: I never dreamed I would be saying something like this because I have fought for the First Amendment in the courtroom. But one of the means that has supplied oxygen to ISIS for both recruitment and inspiration has been the internet. It has been Facebook. It's been Twitter.

And, you know, these are private U.S. -- not private, public U.S. corporations. They started here.

You know, is it not time for some leader to at least bring this group, these corporations to find, figure out some way to shut down that inspiration, that recruitment.

GIULIANI: A President Kennedy, or a President Reagan or President Bush, or a president would have called them into the White House a couple years ago and said let's cut the -- we don't need to tell anybody, but let's stop all -- what do you want to be?

You want to be an instrument of murder? An instrument of killing? But, honestly, that's not the root cause of the problem. The root cause of the problem is them and if they don't communicate through those means, they will communicate through other means.

That just makes them more effective. We have to wipe out ISIS. When Franklin Roosevelt declared war against Nazism, he didn't put a timetable on the war. The war was when they were defeated completely. When Abraham Lincoln went to war, it wasn't, you know, we're going to be in this war three years. It was we are going to fight this war until the union is kept together. This president doesn't understand.

VAN SUSTEREN: In World War II, it was, you know, a number of nations that joined together to fight Hitler. You know, it seems to me that to fight ISIS, it would be, it would be very helpful if we had a real leader, a super power to sort of, you know, get the other ones on board.

I mean, President Hollande seems like he's quite willing and President Cameron, they're both -- Prime Minister Cameron are quite willing.

Who would be more likely to be respected by world leaders to try to help lead that? A President Clinton or a President Trump?

GIULIANI: President Trump, of course. I mean, she is the one who presided over the overthrow of Gaddafi in Libya. And look what we have in Libya. She reset the relationship with Russia.

Look at how bad the relationship with Russia is since she reset the relationship.

Look, Hillary Clinton has had her chance to conduct the foreign policy of the United States and she has been, I will say, kindly a disaster. Every single thing she touched as secretary of state, whether it was her policies or Barack Obama's, they are the same, ended up worse.

The Middle East is worse. The relationship with Russia are worse. Eastern Europe. I'm not even going to mention the South China Sea and the disaster.

VAN SUSTEREN: It's interesting to look at what she said this week. She said that ISIS is not to be contained, it's to be destroyed. Which I actually thought was a departure from --

GIULIANI: It was.

VAN SUSTEREN: But I though, you know, I didn't know to what extent she had been a loyal sort of civil servant to president as secretary of state. She's been out for four years. And now she's sort of moving out along, because she is a little hawkish than President Obama.

GIULIANI: Well, look, I don't believe her. I don't believe that the public opinions polls turn. Look, she voted for the war in Iraq, and then she was against the war in Iraq and was in favor of the timetable when public opinion turned.

So, you know, she reset the relationship with Russia and that was ridiculous thing to do. And she got nothing in return for it. I once asked Secretary Gates what did you get in return for the reset of the relationship with Russia, his answer was nada.

Well, that's not negotiation, that's a capitulation. And this woman is a complete slave to public opinion polls. So, if she were to engage in a war with ISIS and two years into that war, things got ugly, and American public opinion changed, she would do what she did in the Iraq war. She put a timetable on it. We leave and we make things worse.

We need a president like Abraham Lincoln who, when American public opinion was against the civil war in 1863, didn't put a timetable on it. When there were draft riots in New York, and even though he was going to lose New York, possibly, as a state, and he needed it to get re-elected, Abraham Lincoln didn't quit the civil war because well, we can only take three years of the war.

Well, these people have come up with this insane notion of putting a timetable on war. And the timetable gets determined by polls.

I don't know, you know, the Battle of the Bulge, we might have made sort of a compromise with Germany at the Battle of the Bulge because it was so bad for us. If we didn't have a president and General Eisenhower who said the heck with that, we're going to continue it and we're going to win this until we have complete, absolute victory.

I do not trust her to do that for my country because she has proven to me time and time again, she is untrustworthy. And 65 percent of my fellow citizens and yours agree with me that she is untrustworthy.

VAN SUSTEREN: Mr. Trump has got some bad numbers, too, going in November.

GIULIANI: Well, I'm willing to give a guy a chance, who hasn't already shown me that he has failed at it.

VAN SUSTEREN: Mr. Mayor, thank you for joining us.

GIULIANI: Thank you.