The following is a transcribed excerpt from 'FOX News Sunday,' September 5, 2004:

CHRIS WALLACE, FOX NEWS: Labor Day weekend used to be the traditional start of the presidential campaign. Of course, President Bush and Senator Kerry have been hammering each other for months, but we thought this is still a good time to look at where the race stands now.

First up, the man who gave a rousing speech last Monday night at the convention, former New York City Mayor Rudy Giuliani, who joins us from our Fox News studios in New York.

And, Mr. Mayor, welcome. Thanks for coming in today.

RUDY GIULIANI, FORMER NEW YORK MAYOR: Good morning, Chris.

WALLACE: Let's start with the two new polls taken during and after the Republican Convention. Time magazine finds that in a three- way race, President Bush now leads Senator Kerry 52 percent to 41.

GIULIANI: Right.

WALLACE: And a Newsweek poll has exactly the same results, Mr. Bush leading by 11 points — that, incidentally, a 13-point swing in the last month.

Mr. Mayor, what's happened to this race?

GIULIANI: Well, I think, you know, a lot of that, I'm sure, people will attribute to the convention, but I saw that kind of happening maybe a week and a half before. I was campaigning with the president in New Mexico about a week before the convention, and it seemed to me at that point that the whole thing had turned already.

And the crowds that the president had were almost like pre- election crowds. It was almost as if we were in the four or five or six days before the election.

So I think that, you know, the momentum is going in the president's favor. The convention was usually successful. I mean, it was a convention about which there was a certain amount of concern because it was in New York, because of the issues of terrorism and protests and all this other stuff, Democratic stronghold. Turned out to be one of our most successful conventions ever.

And the president's speech on Thursday night was like a State of the Union speech, except with a lot more emotion, you know, particularly in the second half of it.

He laid out a very specific agenda, or as specific as you're going to get in an acceptance speech, much more so than John Kerry did. It was almost as if he was the challenger and John Kerry was the incumbent.

WALLACE: But, Mr. Mayor, if you say that you think the dynamics changed during August, the only thing that happened then was the Swift Boat controversy. Do you think had...

GIULIANI: It's not so much the controversy itself; it's the way in which John Kerry handled it, which was kind of fumbling it, first not answering it, then answering it too much, and then turning it into an attack on President Bush and trying to make a connect-the-dots sort of argument to President Bush when, in fact, it doesn't work.

I mean, this is an independent thing that's going on. It shouldn't go on; I'm against it. I don't think those ads should be out there, particularly with regard to his record, because I believe he was a hero and he's entitled to that. And President Bush does, and President Bush has made this point.

But, I mean, now he's become kind of really personal, you know, really strong attacks on both the president and vice president. So I think the whole way in which it's moving is moving very much in the president's favor.

Plus, the president, you know, on the fundamentals, the president, I think, is — every time he gets his case out, we're going to do better and better. We were getting pounded for six, seven months, $70 million in negative commercials. This was the first chance that we really had to lay out the president's case, and it's a very powerful one, after all.

WALLACE: Mayor, let's go back to your speech on Monday night in which you talked a lot about the events after 9/11 and the decisions that the president has made since 9/11. And you took us back to that moment when the president visited Ground Zero and then said, as he was speaking to that crowd, that the whole world, the terrorists especially, are going to hear from all of us. Let's watch a clip from that speech.

(BEGIN VIDEO CLIP)

GIULIANI: So long as George Bush is our president, is there any doubt they will continue to hear from us?

(APPLAUSE)

We owe that much and more to the loved ones and heroes that we lost on September 11th.

(END VIDEO CLIP)

WALLACE: You seem to be saying that we owe it to the victims of 9/11 to re-elect George W. Bush.

GIULIANI: No, to conduct the war on terror. And then, at least the way I see it, my opinion is that the best way to conduct that war on terror to its successful conclusion is to elect President George W. Bush. It would be no different than saying in the middle of the Civil War that the best chance of winning the Civil War was to re-elect Abraham Lincoln.

WALLACE: Let me switch, if I can, from the national security side to the domestic side, because there was less emphasis on that in the convention. And Democrats say that the president has a lot to answer for on the Democratic side. Let me give you a couple of examples here.

1.3 million more people living in poverty last year; 1.4 million more without health insurance; 900,000 jobs lost since Mr. Bush became president.

Mr. Mayor, is that a record to run on?

GIULIANI: Sure, I mean, because you have to look at the rest of the record. The rest of the record is we've been gaining jobs steadily now for 10 months or more, I think it is. Certainly the last month, a good, solid gain.

Our economy is growing at levels that are better than most of the rest of the world. We're at about 4, 5 percent. Unemployment keeps going down. This month it went down again.

So you have to understand where the president, you know, took over. He took over in the middle of an economic downturn. Then we got hit horribly on September 11, 2001. Obviously, the human part of it being much worse, but the hit to our economy, you know, very, very substantial, dramatic. In fact, you wonder how a economy could recover this quickly after what happened to us on September 11. Then the corporate scandals, a lot of other things.

Well, he's gotten us through it. His tax cuts have helped. His tax cuts are fueling our economy and we're growing again.

So I think it's a very strong record, given in actuality what happened. Again, it's like going back to Franklin Roosevelt during the Depression. You know, Franklin Roosevelt was re-elected in the midst of the Depression, and we hadn't gotten out of the Depression. He had just made progress. We didn't get out of the Depression until really until the Second World War.

WALLACE: Let me ask you about another domestic issue, if I can. The administration announced it late on Friday of Labor Day weekend, but Medicare premiums are going to go up 17.5 percent next year, which is the largest increase in 15 years. Is that a record to run on?

GIULIANI: Well, also the coverage is going to be expanded, and the fact is that those are formulas in which there are uncontrolled costs. And this has been the biggest expansion in health care that anyone has ever been able to accomplish.

GIULIANI: So, I think, you know, what you have to look for in a president is realistic progress. Our economy is making substantial progress, given the situation that it is. You would have to regard our economy now as growing. Jobs are growing. The whole economy is coming back.

And then, really, it's a choice for the American people: Do you agree with the philosophy that it's better to put money back into the private economy, or do you agree with Senator Kerry and Senator Edwards that the best thing to do is to raise taxes?

And you know they're going to raise taxes on everybody, because they can't possibly pay for what they're promising, even come close to it, without raising taxes substantially.

WALLACE: Mr. Mayor, we've got about a minute left. I want to ask you about one other part of the Newsweek poll, if I can.

Fifty percent of registered voters and 65 percent of Republicans say they'd like to see you run for president in 2008. And that, you'll be happy to note, puts you ahead of John McCain and even Arnold Schwarzenegger, if the Constitution would change to allow foreign-born citizens to run.

(LAUGHTER)

So, Mr. Mayor, my question is, when you look in the mirror, do you see a potential president?

(LAUGHTER)

GIULIANI: I haven't — actually, I rushed so hard to get here this morning, I didn't get a chance to look in the mirror. You know, I had to be here on time.

But John McCain and Arnold Schwarzenegger are two people I admire very much. I'm not — the race for the presidency four years from now is so far away, I'm not thinking about it, I'm not running against anybody.

Right now there's only one race. It's get President Bush and Vice President Cheney reelected.

And, you know, Arnold Schwarzenegger's doing a great job as governor of California, and John McCain is one of my heroes. So I don't want to be in any kind of contest with them.

2008 is such a long way away. We'll see who runs, and we'll see who the best candidate is. You know, it'll be some time from now.

WALLACE: All right. Mr. Mayor, thanks so much. We appreciate it.

GIULIANI: Hope to see you soon, Chris.

WALLACE: Yes, please, come on back.

GIULIANI: Thank you.