The following is a partial transcript of the June 11, 2006, edition of "FOX News Sunday With Chris Wallace":

"FOX NEWS SUNDAY" HOST CHRIS WALLACE: Joining us now, live from Baghdad, is General George Casey, the commander of multinational forces in Iraq.

General Casey, welcome back to "FOX News Sunday". Sir, take us back to Wednesday night and tell us about the order to launch the attack on Zarqawi.

GEN. GEORGE CASEY: Well, first, good morning, Chris. Nice to be back with you. And as you can imagine, it's been a good week here in Iraq. I think you've heard probably the stories, but Wednesday evening — late afternoon, early evening — an operation that had been in progress for weeks came to bear fruit.

And we had been tracking one of the individuals, one Sheikh Abdul Rahman, personally for almost two or three weeks. And he was tracked to a house just about eight kilometers north of Baquba, which is just outside of Baghdad, to the north, and there were significant signals that he was there to attend a meeting with Abu Musab Al-Zarqawi.

One of my commanders gave me a call, told me what he was going to do, and I said go ahead, and he struck the house. He went with an air strike because of the isolated location of the house and it's a very wooded palm forest area, and only one road in and out. So there was concern that if we tried to get in there by ground, we'd be discovered and he would escape yet again.

So it was a very successful day for us. It's a great loss to the network. But I think everybody's been quite clear here that it's not going to end terrorism in Iraq. But it's certainly taken out the number one terrorist that we've been after here for three years, made it a great day for the Iraqi people and a great day for us.

WALLACE: If I may ask you, on a personal basis, you've been fighting this guy for two years over there in Iraq. What were your personal thoughts when you got the final confirmation you got him?

CASEY: It's interesting, because I wouldn't let myself believe we really got him until we got the fingerprints back. And so that was not till about 3:30, 4:00 o'clock in the morning when we got that call. But I was actually — frankly, I was quite happy.

WALLACE: I'm sure. Al Qaeda in Iraq has posted a message on an Internet Web site today in which they promise to continue to carry out, quote, "major attacks that will shake the enemy." Your reaction, sir.

CASEY: That's expected. They are hurt badly. And it's not just the Zarqawi operation, but we have had a series of operations in the aftermath of that based on intelligence we have gathered over the past weeks while tracking this one individual, and we have had a steady drum beat of operations against the Al Qaeda network here in Iraq since the Zarqawi operation.

I expect them to say what they said. I expect them to try to do what they said. But I think what you're going to see is an enhanced security operation here announced by the prime minister in Baghdad over the course of the coming week and a tightening of security in the Baghdad area.

So like you said, it's expected, but I think we'll be prepared for it. But again, you can't stop terrorist attacks completely.

WALLACE: According to the U.S. government, there are more than a dozen insurgent groups in Iraq and, again, according to U.S. government estimates, Zarqawi's forces represent only about 1,000 of the 20,000 fighters in the insurgency.

Given all of that, what can you say about the impact that Zarqawi's death has had on the insurgency in general and also the sectarian violence that he was so devilishly effective in helping to foment?

CASEY: As you suggest, he does not have great influence over the primarily Sunni insurgency, so the impact on that will not be great. He does and did have quite a lot of influence on his own network, which is foreign fighters and some large number of Iraqis.

It is a network, and so I'm sure there are plans and operations that are out in the different cells of that network that are still in training, and they will still attempt to conduct them. But they lost their leader. And any organization, particularly an organization at war that loses their leader, is effective.

And we will continue to go after his network and disrupt it in what we feel is a very vulnerable period. And so we hope to take advantage of that. Now, again, it's not going to stop terrorism across Iraq, but it is a major blow to both his network and to Al Qaeda.

WALLACE: General, let's try to tie up some loose ends and let's blast through these as a kind of lightning round. First of all, have you gotten back the results of the DNA tests and can you, in fact, confirm that it was Zarqawi?

CASEY: We have not gotten back the results of the DNA test. However, we have very clear visual identification. We have a 100 percent match on the fingerprints, and we have a good match on scars and tattoos on the body.

So I am very, very confident that we have killed who we said we've killed.

WALLACE: General, we understand that the autopsy of the body has been completed today. Do you know what those results show? And how do you respond to this claim by at least one Iraqi man who was on the scene that he saw Zarqawi's body being beaten before he died?

CASEY: I have not seen the results of the autopsy, and the way I respond to the comments of the alleged Iraqi who saw what went on there is that's baloney, and we've already gone back, looked at it. Our soldiers who came on the scene found him being put in an ambulance by Iraqi police. They took him off, rendered first aid, and he expired.

And so he died while American soldiers were attempting to save his life. And so the idea that there were people there beating him is just ludicrous.

WALLACE: General, starting tomorrow you're going to be participating in this two-day war council, the president and all of his war cabinet, up at Camp David — also top Iraqi officials. How wide-ranging will the review be? Is everything on the table?

CASEY: Chris, you'd have to ask Steve Hadley that. We're going to provide — obviously, Zal Khalilzad and I will provide an assessment of how we see things going from here. But I think you'll have to talk to the White House on exactly how wide-ranging it's going to be.

WALLACE: Now, the White House keeps saying and the president has said continuously that he's going to make any decision about how to proceed based on the advice, frankly, from you, from the commanders on the ground.

Is it possible that we could end up not with troop cuts, but, in fact, with more troops?

CASEY: Are you saying as a result of this meeting, is that possible?

WALLACE: Yes.

CASEY: It's not likely. But as I've said all along, I constantly evaluate the situation. And if I think I need more, I'll ask for more. If I think I need less, I'll tell the president I need less. So that would be my answer to you.

WALLACE: Are you going to tell him tomorrow whether you need more or less?

CASEY: No, I'm not going to discuss what I tell the president, Chris, with you...

WALLACE: Well, I...

CASEY: ... as close as we are.

WALLACE: As personally close as we are. General, you mentioned, though, the fact that Prime Minister Maliki — one of the main operations that he's already begun to talk about, and I know you're already working with him about, is the idea to secure the capital of Iraq.

Now, as you know far better than I do, there have been these operations in the past — Operation Lightning a year ago. In fact, recently you called in more troops to — I think 1,500 more troops to Anbar province because you felt you needed them. May you need more U.S. troops to help secure the capital of Baghdad?

CASEY: It's possible, Chris. Right now we're not planning on it, but it's possible. I will tell you the big difference in this operation is going to be the fact that it's being conducted by a national unity government.

And he has the opportunity to bring the power of that unity to bear on the security situation in Baghdad and to have those political leaders engage the population in support of the operation.

And candidly, we've not had that before, and so this is a new dimension and it's what the patience of waiting for this national unity government I think can help us do.

WALLACE: Do you think that it's important for the unity government to get out from behind the barricades of the Green Zone and, in effect, operate, live, in Baghdad like all of the residents?

CASEY: Absolutely. I mean, the leaders need to be in touch with their population not just in Baghdad, but around the country.

And I think an indication of how this prime minister is going to be — as you saw, I think he went to Basra on his first week in the job, which is the second or third city in Iraq. And he went there to address the security situation right out of the box.

So I think you're going to see this prime minister be very active and aggressive in moving about the country talking to his people.

WALLACE: General, all sides say that another key objective is that you've got to clean up the police, and you've got to get rid of the militias both on the street and inside the police.

Now you finally have a new interior minister, Jawad al-Bolani. How do you break through this cycle where various groups feel that they need militia to protect them, to get them out of the street, to get their arms gone and also to get them out of the police?

CASEY: A couple of things. First, the other really good thing that happened last week, as you suggest, was the completion of the formation of the government and the appointment of the key security ministers, the minister of state for national security affairs, the minister of interior and the minister of defense.

We met with them yesterday. We had dinner with them last night. And I will tell you, I left that initial session with them with a firm impression that we've got bright, articulate, hard-charging folks that are going to take charge of these ministries and move the country in the right direction.

Secondly, again, I go back to the function of unity and what a national unity government is able to do that other governments here have not been able to do.

And when the minister of interior for this government is able to leverage the political influence of all of the leaders of the political parties to help reduce the influence of militia, and particularly to reduce the influence of militia on the security forces, that is going to be extremely helpful.

The other thing I think you're going to see from this minister is the very aggressive hands-on approach. He went to his office straight off the bat and spent that night driving around Baghdad inspecting the ministry of interior checkpoints that were out there.

And that's what the Iraqi security forces need to see. They need to see an aggressive leader who's interested in them and who is interested in national unity.

WALLACE: General Casey, we've only got about 30 seconds left. One final question. As we look back at the successful attack against Zarqawi, the formation of this new government — again, we've got 30 seconds left — where do you think Iraq is and the U.S. mission is right now in Iraq?

CASEY: I think we're in a position to begin moving this campaign and helping the Iraqis move this country in a very positive direction. And we've worked hard to get to this national unity government. They're in the lead. They have our full support. And I think you're going to see this government start moving forward.

It will not be without fits and starts, but I believe they have the capability to move this country in the right direction.

WALLACE: General Casey, thank you so much for sharing your Sunday with us. Thanks for appearing on our show.