This is a partial transcript of Special Report with Brit Hume, August 13, that has been edited for clarity. Click here to order the complete transcript.

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BRIT HUME, HOST: The continuing series of terrorist-style attacks on US and coalition forces in Iraq has raised an intriguing question: Has the US, which went to war against a regime thought likely to help Middle East extremists (search), ended up fighting those very extremists themselves?

For answers, we're pleased to be joined from Baghdad by Ambassador Paul Bremer, the US Administer, in Iraq.

Mr. Ambassador, what about that? Is Iraq now turning out to be a theater in the actual war against terrorists?

PAUL BREMER, IRAQI CIVILIAN ADMINISTRATOR: Well, we certainly have got a lot of terrorists coming into the country. Most of them appear to be the guys who we didn't kill when we attacked in Ansar al Islam base, in the north of Iraq, at the beginning of the military operations. The ones who survived fled over into Iran. And they seem to be filtering back into Iraq now. And it's a substantial…it's a substantial threat, I think. There's no question.

HUME: What about…have they been given help and support and safe passage, to some extent, by the Iranian government?

BREMER: It's a little hard to tell the degree of Iranian government involvement with them. This is a group, after all, which is more closely aligned with Al Qaeda (search). And therefore, it's sort of sectarian interests go more towards the Sunni, than towards the Shiia side.

HUME: Let me ask this question, in a somewhat different way. These may be people the United States was going to have to fight anyway, somewhere. So, is it is a bad thing or good thing that they have come into Iraq to take on the American military?

BREMER: Well, you know, obviously speaking for those of us here, in Iraq, it doesn't look like a very pleasant alternative. But I have to say, from a national point of view, if we're going to fight terrorists, and we have to, we would, I'd rather have us fighting them somewhere outside the United States, than fighting them inside the United States.

And if we can capture or kill these guys here, that's fewer people who are likely to fly planes into buildings in the United States. So, from a…from an overall national security point of view, we've got war on terrorism. And we're going to have to fight it where we can find the terrorists. And we're finding them here now.

HUME: What about security now in Iraq? Just today, the esteemed columnist of the The New York Times, Thomas Friedman, wrote about being held up on the road coming into the country: thousands of dollars taken, AK-47 muzzles in their faces. Talked later to US soldiers they met down the road who said, sorry that happened we just don't have enough people.

In your view, do we have enough people to do the job in terms, of securing that country?

BREMER: Well, I think we do, and I think it's important to keep this in a bit of perspective. I'm…I'm obviously sorry for Mr. Friedman. He got robbed right after he left me, actually. I think he was leaving the country that night but most of this country is at peace, Brit. And it's…it's important not to be taken in by stories of this country being in chaos. It's simply not true. All of the big cities here are operating normally, a lot of commerce during the day.

It's true. There is crime at night. You got to remember that Saddam (search) let more than 100,000 prisoners, hardened criminals, murderers, burglars, rapists out of jail, before the war. And we've got to capture these guys sooner or later. There is a lot of crime. There's no question about that. But basically, we do have enough troops to do the job that needs doing.

HUME: Are you saying the infiltrators we've spoken about, from Iran, are not part of these groups? Is this an additional force?

BREMER: That's…That's right. That's right. We have a...

HUME: How many do…overall, Mr. Ambassador, do you have…can you give me some estimate of how many of these terrorist-style operators there are? Are we talking about 100’s of them, 1000’s of them, tens of 1000’s? What?

BREMER: No. I think we're talking probably 100 or maybe a few more than 100 of these Ansar al Islam terrorists. The…there are, some other…one might call them, other foreign fighters, non-Iraqis who have…some of them came in, to support Saddam, before the war. And there's been some infiltration, particularly across the Syrian border of others. We've captured and killed some of those.

But the people who are attacking our soldiers, so far, have not been these terrorists. I don't…I don't say they're not a danger to our soldiers, and for our civilians. I think they are. But the attacks that you read about, the use of explosive devices, the machine gun attacks on our soldiers; these are being conducted by the professional killers from Saddam's regime, who incidentally, again, so far as we can tell, are not operating with any central command and control. These are small squad- level operations we're seeing.

HUME: And how much progress do you believe that has been made in identifying, finding, and eliminating these threats, these people, these fighters?

BREMER: Well, I think we've actually had a pretty good month. What…what we saw starting, just before the…the information leading to the deaths of the two sons, Saddam's two sons we've seen an increase of Iraqi citizens reflecting the confidence they feel in our forces coming in and telling our forces about where the bad guys are. More and more informants coming into the Iraqi police, coming into our tactical commanders.

And interestingly, Brit, in the last 10 days or so, an increase in the number of former regime officials, from the Ba'ath Party, from the Fedayeen Saddam, from the intelligence services, increasing number of these guys coming in, and simply turning themselves into our commanders. I interpret that to mean that they're beginning to say to themselves, you know, I really don't want to die the way Uday (search) and Qusay (search) did. I can see that the new Iraq is going to succeed. And I…I don't want to be dead, I'll just take my chances by turning myself in.

So, I think there's some indicators that things are a…are on the move here, on the security side.

HUME: Mr. Ambassador, thank you very much.

BREMER: Nice to be with you.

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