This is a partial transcript of "Special Report with Brit Hume", June 16, 2004 that has been edited for clarity.

Watch "Special Report With Brit Hume" weeknights at 6 p.m. ET

BRIT HUME, HOST: There are now some indications that Abu Musab al Zarqawi (search), the most-wanted man in Iraq, as far as the U.S. is concerned, may now be operating from in and around Fallujah. Fallujah, of course, was the disputed city, the heart of the Sunni Triangle (search), where there was so much trouble and where the Fallujah Brigade, a group of Iraqi officers and others have been in charge for some time now.

For more on Fallujah and on the possible whereabouts of Zarqawi, we're pleased to be joined now by Brigadier General Mark Kimmitt, who is the deputy director of coalition military operations in Baghdad.

General, what can you tell us about this -- these reports that Zarqawi may now have found a place to operate in and around Fallujah?

BRIG. GEN. MARK KIMMITT, DEPUTY OPS DIR., U.S. MILITARY: Well, Brit, for quite a long time, we've looked at Fallujah at one of those areas where the Zarqawi network has been operating out of. We've had significant intelligence that says this is one of those places that Zarqawi himself may be operating out of. So we've watched this area very closely, and we're collecting the intelligence to strike at and when the time comes.

HUME: Would it be fair to say that the objectives that the coalition had when it turned over the control of that city and the policing of that city to the Iraqis, have not been met? Or perhaps you can tell me which ones have been met. I know you wanted to obviously to pacify the town.

You wanted also to try to do what you could to break up that terrorist network operating there. You wanted, I know also, to bring about the capture so you could discipline, so to speak, the people who were responsible for the murder of those four Americans, whose bodies were so hideously treated after they -- after they had killed them. What about those objectives? How have they been met?

KIMMITT: No. I mean I think at this point it's a mixed report card. We were very clear and remain clear in the coalition objectives in Fallujah. We want the Iraqi control inside the city. We want the foreign fighters out. We want the heavy weapons out. And we want those who were responsible for the 14 February attack on the police station and the attack, where they cruelly killed and dismembered the American contractors brought to justice.

Right now we've got somewhat Iraqi control back in the city. We haven't met those other objectives. But it's important also to recognize that ever since the discussions that were brought about by the Sunni leadership, there hasn't been any firing going on. There hasn't been any loss of life, nor bloodshed since May 3. And so that's a good thing. It is quiet, but honestly and correctly as you identified, we have not yet met our objectives. But we continue to pursue those objectives every day.

HUME: Well, let's look at them one-by-one. What about breaking up or taking Fallujah out of play as of -- as a base for terrorist operations against the U.S.? What about that?

KIMMITT: Well, certainly we can't say we've achieved that yet. We don't have full Iraqi control in that city. And until we have Iraqi control and coalition presence in those cities, and more importantly, Iraqi security presence in those cities, we feel comfortable that the city doesn't remain as a potential hotbed of terrorist activities or anti- coalition activities.

HUME: Do you have any reason to believe that a serious effort has yet been made to capture those who were responsible for the attack back in February, and also for the mutilation of those Americans who were killed then?

KIMMITT: Well, I don't think we're going to be able to judge the results of that effort until we have those people under our control.

HUME: So, in other words, you'll know it when it happens. Until then, you don't know how hard they're trying?

KIMMITT: That's correct.

HUME: All right. Let's talk a little about what your options are. Do you believe -- first of all, do you believe that it's possible or safe to turnover sovereignty to the Iraqis, with a place like Fallujah still festering to the extent that it is?

KIMMITT: Well again, we are going forward with the transfer of sovereignty on June 30. The Iraqi authorities who were instrumental in achieving the goals that we've reached, so far in the conditions that we currently have in Fallujah, are very comfortable with assuming sovereignty on 30 June despite the fact we have unfinished business in Fallujah.

HUME: Now, if the Fallujah Brigade, so called, which is in charge there now, or is supposed to be in charge there now has not done the job, what can you do?

KIMMITT: Well, we can continue to encourage. We're going to continue to work side-by-side with them. We're going to continue to do as General Mattis did the other day. Go into the city, sit down with the leaders, let them understand that the future of Fallujah is to a great degree in their hands.

There's a lot of money that can be spent in Fallujah. There's a lot of peace, prosperity and progress that can be brought to Fallujah with much of the money that's been provided by the American taxpayers and others.

HUME: This is reconstruction money, correct?

KIMMITT: And they have got to decide whether they want to enjoy that -- that's reconstruction money. That money can be put in Fallujah, or it can be put somewhere else. That's a decision that people of Fallujah, but more importantly, the leadership of Fallujah has to make.

HUME: It sounds, general, as if a military option for -- action by the United States -- I'm talking about major military undertaking there is off the table, is that correct?

KIMMITT: No options are off the table. Clearly, we would seek to achieve a peaceful resolution. But we're always going to maintain and retain military option for Fallujah.

HUME: Well, it seemed that the reason that the military option was decided against the first time around, was that the military situation was such that any major military invasion, or incursion into the city by our forces, it would be enough to get the job done, would necessarily result in a lot of destruction and civilian loss of life. Is there anything changed -- has anything changed that?

KIMMITT: Well, that was certainly the perception that was brought forth by the Sunni leadership, by the Iraqi leadership that came forward and said look, instead of laying siege to this city, instead of having a major offensive operation inside the city, which might also have a collateral affect on the rest of the Sunni Triangle, let's try to resolve this peacefully. It won't come as quickly as you may like or as you may like. But it may be done with far less loss of life and far less destruction of the city.

HUME: So for the moment, your posture is you watch and you wait. And how much time do you think can you give this?

KIMMITT: We want to see progress every day. Some days we see progress. Other days we don't. But until a series of days go by where the commanders on the ground don't see sufficient progress, until we don't see a full-faith effort on the part of the Fallujah leadership and the Fallujah Brigade to keep moving forward, I think we'll continue to let this process move forward even past June 30. That's not only our desire, but that is certainly the strong desire of the interim government of Iraq.

HUME: All right. General Kimmitt, thank you very much for joining us.

KIMMITT: Sir, thank you.

Copy: Content and Programming Copyright 2004 Fox News Network, L.L.C. ALL RIGHTS RESERVED. Transcription Copyright 2004 eMediaMillWorks, Inc. (f/k/a Federal Document Clearing House, Inc.), which takes sole responsibility for the accuracy of the transcription. ALL RIGHTS RESERVED. No license is granted to the user of this material except for the user's personal or internal use and, in such case, only one copy may be printed, nor shall user use any material for commercial purposes or in any fashion that may infringe upon Fox News Network, L.L.C. and eMediaMillWorks, Inc.'s copyrights or other proprietary rights or interests in the material. This is not a legal transcript for purposes of litigation.