The following is a partial transcript of the July 30, 2006, edition of "FOX News Sunday With Chris Wallace":

"FOX NEWS SUNDAY" GUEST HOST BRIT HUME: With us now to discuss the situation in Iraq is Ambassador Paul Bremer, who is the former administrator of the Coalition Provisional Authority set up just after the conquering of Baghdad.

Welcome back to "FOX News Sunday", Mr. Ambassador. Nice to see you.

AMBASSADOR PAUL BREMER: Nice to be with you again.

HUME: Assess for us, if you will, the current situation based on your experience there. How does it look? Baghdad looks bad.

BREMER: Yes, it's pretty discouraging, I think. The new prime minister, whom I know made an announcement, I guess, five or six weeks ago about putting a priority on securing Baghdad — I think that's important. It's the capital. Not much happened until he came here this week.

I gather now that as a result of the conversations with President Bush, we're going to deploy a Striker brigade. These are a new kind of armored vehicle. I drove around the city of Mosul in one of these in its first deployment to Iraq, and I hope that will help. That's going to add another brigade to Baghdad. It's very important.

HUME: Yes, we're talking about something like 3,500 troops, give or take.

BREMER: Right.

HUME: Given the situation in Baghdad, a city you know well, given the number of forces already deployed there, the number in the tens of thousands, is this enough to make a difference against this — the continuing violence there?

BREMER: Well, you know, Brit, the question has gotten a lot — and I've been part of that, unfortunately — focused on the number of troops. The real question is how are they deployed, and what are their rules of engagement and what is the strategy for using them. That's the real question.

Now, as I understand it, the prime minister plans to try to use these new forces and the Iraqi forces to, in effect, go neighborhood by neighborhood, try to secure a neighborhood and then work out from that area and work around. And I think that's the right approach.

HUME: Well, what does that mean? Does that mean you're knocking down doors and...

BREMER: It will depend on the neighborhood. One of the key problems...

HUME: Can you do this kind of pacification of an area...

BREMER: Yes.

HUME: ... which is as violence-prone as Baghdad is without really playing rough?

BREMER: No. No, no. They will have to play rough, to use your terms. They're going to have to deal sooner or later with the Shia militia in particular.

And it was encouraging to hear the prime minister in his statements here both in the press conference and in the Congress say very clearly that he understands they're going to have to go after and disband these militia.

HUME: Well, you're talking about militias such as the Sadr militia.

BREMER: Muqtada al-Sadr's militia in particular, the Mahdi army. That's the most important one.

HUME: Now, that's a big one. Is it your sense that the Mahdi army is responsible for a lot of this violence?

BREMER: Yes.

HUME: Sectarian violence? It is?

BREMER: Yes. Clearly.

HUME: All right. Now, so what needs to be done? Are you going to go in there and kill those people? Is that how you do it, or what?

BREMER: Well, you're going to have to kill some of them. You're certainly going to have to kill the leaders or bring them to justice one way or the other.

HUME: What about Sadr himself? He's a very large figure in Iraqi politics.

BREMER: He is a large figure, and they will have to find a way to deal with him. He's now got some political importance. One of the problems for Prime Minister al-Maliki, himself a Shia, is, of course, he's under some pressure from these radical Shia like Muqtada al-Sadr.

HUME: So what about him? He was somebody we had in our gun sights, so to speak, while you were there. Should he have been killed?

BREMER: The proposition wasn't to kill him. The proposition was to allow the Iraqis to execute an arrest warrant. He was accused...

HUME: That's right.

BREMER: ... by an Iraqi judge of murdering a very respected ayatollah, Ayatollah Khoei, a couple of days after the liberation of Baghdad. There were eyewitnesses that accused — basically said Muqtada ordered this murder. And an Iraqi judge issued an arrest warrant. The question was whether to arrest him, and we were unable to do that during my time.

HUME: Well, you were unable to, or was a decision made not to?

BREMER: It was a combination of both.

HUME: Who wanted to do it and who didn't?

BREMER: Well, I was very much in favor of arresting him, allowing the Iraqis to arrest him, a number of times because I feared that he would develop into an anti-democratic Shia extremist force in Iraq, which unfortunately has happened.

HUME: Let's turn to — you mentioned this issue of number of troops. It has come up time and again.

It has become, I think, almost received wisdom now about the original plan there and the post-fall-of-Baghdad period when you were there that the United States simply didn't have enough troops to do what needed to be done, that General Franks' plan — it was brilliant for the accomplishment of the task of toppling Baghdad and ending Saddam's regime — was simply inadequate to the task that inevitably came after. Your view of that in terms of troop numbers.

BREMER: Let me start with the basics. The basics are that the role of any government — and we were the government of Iraq — is to provide security for its citizens, law and order. And when I arrived in Baghdad, there was widespread looting going on in Baghdad, and we weren't stopping it.

In fact, we had enough troops. We had 40,000 American troops in Baghdad at that time, but they didn't have orders to stop the looting. So the problem wasn't immediately the question of the number of troops. It was what are their rules of engagement, as the military calls them.

And that problem, I think, that — the fact that we didn't stop that looting right away in the very beginning, the first month or so of — after liberation, left the impression with a lot of Iraqis, and perhaps with insurgents, that we were not prepared forcefully to enforce law and order. And I think that was a mistake.

HUME: Now, there's a whole other set of ideas about what went wrong in Iraq. A lot of it is set forth in a new book by Tom Ricks, the well known defense correspondent for the Washington Post, a book whose title kind of gives away what he ultimately thinks about it. "Fiasco" is the title.

Nonetheless, it is a pretty extensive piece of work with a lot of reporting in it, a great many interviews and a lot of detail, pretty rich volume. And he comes down hard on you on a couple of key points.

One was the — what he says was the dissolution of the Iraqi military, that that was a mistake because it alienated these people, and then you had, you know, thousands of armed disaffected men in the streets. What about it?

BREMER: It's not a new argument. In fact, I call this sort of a cat-like issue. It seems to have nine lives. And no matter how many times I answer with the facts, it still comes back.

But let's look at the facts. Let's take a minute. There was no Iraqi army to disband. The Iraqi army basically self-demobilized, as the Pentagon said. There wasn't a single unit standing anywhere in the country. So the question was should we recall the army. Now, let's think about what the army...

HUME: But there was a structure, and there were people who had uniforms and guns and...

BREMER: No, there was no structure. There was no unit left anywhere. There were no barracks anywhere. The army was made up of hundreds of thousands of Shia draftees who hated being in the army. They were brutalized by their Sunni officers. They went home.

There was no army to disband. It had to be recalled. Imagine what the impact of that was politically. This army had conducted a decade-long war of genocide against the Kurds. And I well remember one of my first trips to the Kurdish region.

Massoud Barzani, who's one of the leaders of the Kurdish region, took me for a drive through the area where, as he told me, the army killed 3,000 Barzanis, 3,000 of his tribesmen, during their campaign in the 1980s.

The army was responsible for the killing fields of the Shia — you remember the Shia rose up against Saddam after the 1991 war — and killed hundreds of thousands of Shia. These two groups, the Kurds and the Shia, were cooperating with the American forces.

If we had recalled the army, they would have taken matters into their own hand. Right now, if we think sectarian violence is bad now, imagine what it would have been if 80 percent of the Iraqi people had immediately concluded that we were not real in our desire to replace Saddam's dictatorship.

So the question of recalling the army, in my view, would have been a disastrous decision, and anybody who doubts that needs only look at what happened when the Marines recalled a single brigade, about 1,000 men, of the old army in April of 2004, and there was a political uproar throughout the country that almost threw us off the track of being able to hand sovereignty over in June.

So I'm very comfortable it was absolutely the right decision not to recall the army and to rebuild a new army.

HUME: De-Baathification. The de-Baathification of Iraqi political life is also said to be one of the mistakes.

BREMER: It's another one of these cat-like nine lives...

HUME: I understand, but there it is. It's back again.

BREMER: OK, let's deal with it. Let's talk about the facts. The idea of de-Baathifying in Iraq was very similar to the de- Nazification program we followed in Germany after the second world war. And it's an apt analogy, because Saddam Hussein proudly and openly modeled the Baath party on the Nazi party.

He had neighborhood watch committees. He had children spying on their parents and so forth. Every average Iraqi considered the Baath party to be the important instrument of Saddam's control. That's why General Franks outlawed the party in his April 10th statement after the liberation of Baghdad.

The question of de-Baathification addressed only the top 1 percent of the party. That's what the de-Baathification decree addressed. And all it said about them was you can no longer be on the public payroll. If you're not a criminal, you can go out and set up a business, you can found a newspaper, you can do whatever you want to do, but you may no longer be on the public payroll.

And I don't understand when people criticize this. And by the way, it's overwhelmingly popular among Iraqis, whatever the pundits back here may think.

I don't know how you would explain to the average Iraqi that, having sent our army halfway around the world, throwing out Saddam Hussein, we were going to call back the army that was the instrument of his repression, call back the Baath party, so you went to the ministry, you saw the same old top Baathists in charge of the ministries. It simply doesn't make sense.

HUME: If you have one regret about the way it was run at the time, major regret, what would it be?

BREMER: I think my major mistake in many ways was not this question of troop strength, which has sort of dominated the debate. I think the real problem was that we didn't have a military strategy to defeat the insurgency, and that is what's essential in Iraq now, because the insurgency...

HUME: Do you have it now?

BREMER: I think we've got the beginning of it with this idea of taking control of Baghdad, because the Shia militia, who are conducting most of these attacks we've seen, are reacting to the fact that the government and the coalition have not provided security against the insurgency.

These two things feed on each other. We now need to have a plan, and we have to stay there until it's executed, to defeat that insurgency.

HUME: Ambassador Bremer, pleasure to have you.

BREMER: Nice to be back with you.

HUME: Thanks for coming in.