This is a partial transcript of "Special Report with Brit Hume," July 14, 2004 that has been edited for clarity.

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CHRIS WALLACE, GUEST HOST: Saudi Arabian officials announced today they are ending the search for the body of Paul Johnson, an American who was beheaded by Al Qaeda terrorists last month. But the Saudi's promised to continue cooperation with FBI to bring Johnson's killers to justice. However, the Saudis say Americans will not be permitted to question Kahled al-Harbi, the associate of Usama bin Laden who surrendered yesterday under a government amnesty program.

Where does the always-complicated relationship between the U.S. and Saudi Arabia stand now? How seriously should we take Saudi claims that they're going to crack down on terrorism?

For answers we turn to former assistant secretary of state for Near East Affairs, Edward Walker. He is now president of the Middle East Institute.

And Ambassador Walker, welcome.

EDWARD WALKER, PRESIDENT, MIDDLE EAST INSTITUTE: Thank you. Thanks, Chris.

WALLACE: Thanks for coming in to discuss this. Do you believe the Saudi promises that they are cracking down on terrorism? Do you see signs that they really mean business this time?

WALKER: Oh, I think they're tracking down terrorism. Particularly the terrorism inside Saudi Arabia, and there's certainly been enough firefights and dead officials to prove it.

They also have done a pretty good job now of fixing their financial systems so that they can find where the money is floating out to terrorism. The U.S. gives them a pretty good bill of health on that. I think in March, Coffer Black, our counterterrorism guy said they had probably the most restrictive rules on charities in the world today.

So they make huge progress from zero ground when they started in September 11, but they got a ways to go. A lot of implementation has to take place. They still have a lot of problems.

WALLACE: Let me pick up on what we were just talking about. When you hear that they are not going to allow the FBI to question al-Harbi directly, and we know in the past that they would not give U.S. government officials direct access to terrorists who have even attacked Americans. Does that trouble you?

WALKER: Yes, it does trouble me. And I think it's a mistake on their part. I think they can use the help of the FBI in situations like this. I don't know how much value this man has or would have. He seems to have been out of the picture for a while. Nevertheless, it certainly doesn't hurt the Saudis to cooperate with the FBI, much in the same way they've been cooperating with treasury and the FBI on financing. But there are still big gaps in this cooperation.

WALLACE: So why don't they? I mean they're not worried about public opinion, obviously, in this case. Why not allow the FBI into talk to this fellow or other terrorists?

WALKER: They probably don't know what is he going to say, and they probably want to know that before they start exposing him to other countries' interrogations.

There's also a matter of national pride. I think we all got to get over it now when we're all facing the same enemy. But there are still many states around that feel it's an imposition on their sovereignty to open their doors to foreign investigators.

WALLACE: Now, you talked about some things that the Saudis have done better, especially in the financing area. The Council on Foreign Relations came out with a report last month, in which they commended the Saudis for some areas, specifically the ones you mentioned. But also criticized them for failing to punish any Saudi individual for financing terrorists. And also, I might add, for continuing to export Islamic extremism. Isn't it a very mixed picture?

WALKER: It's a very mixed picture. Part of it is a question of what you call "Islamic extremism." I mean if you are going to define every concept of Wahabism, which is the Saudi brand of Islam as extremism, then they got a problem. I don't think that's quite a legitimate expression.

Certainly there are more radical elements within the Saudi religious authorities that need to be expunged. But you know, the exporting of money and so on is brought under control. And I think that's the key factor here.

WALLACE: Whatever the Saudis are doing, isn't it really much more about responding to the attacks at home, about protecting their own rule than it is helping us or any outrage about terrorism?

WALKER: Of course it is. I mean, you know, this real cooperation didn't start until March of 2003. That's when they were first attacked. Now, that's not unusual for a country to look out for its own interests in the first case. And they have become serious because of the attacks inside Saudi Arabia. But yes, of course, they're more interested in what's going on inside Saudi Arabia and in sustaining the rule of the royal family, and protecting their citizens. That's I think pretty natural.

WALLACE: Is the government strong enough to crack down? Can they really take on the Islamic extremists in the street? Or do they run the risk of a backlash?

WALKER: Well, there is a risk of backlash. But it's more likely to come from movement too fast on the reform agenda, where the religious figures and the traditionalists on the Saudi side rebel. I think they can go full force against the terrorists, though. I think most Saudis are fed up and disgusted by what they've seen the terrorists to do. Particularly beheading of people. Particularly attacks on other Muslims. So I think they've got the people with them in this area.

WALLACE: So briefly, what should we be looking towards in the future that will be an indication they mean business?

WALKER: If you really want the key to it, it's change and reform both in terms of their society and in their education system. That's where the basis of these problems arises. They've got to be able to start changing the way they educate their children, the way they train them. And they've got to pull the religious figures under control.

WALLACE: Ambassador Edward Walker, thank so much for giving us some insight into always-complicated relationship.

WALKER: You bet.

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