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CHRIS WALLACE, FOX NEWS SUNDAY HOST: Good morning, again, and happy Fathers' Day from Fox News in Washington. Let's begin as always with a quick check of the latest headlines.

There's a new report today about the insurgency in Iraq. U.S. officials say in recent months, more of the combatants captured in Iraq (search) are from Saudi Arabia, Syria and other foreign countries.

In Baghdad, a new wave of violence this morning: At least 16 people were killed in a restaurant by a suicide bomber. In two other attacks, soldiers and police officers were targeted. The number of dead and wounded in those incidents was 20.

And in Iran's election, the candidate who finished third and was eliminated from the runoff has charged that that vote was rigged. Iranian officials have not responded to his complaints.

With growing concerns about Iraq, with that election in Iran and word from North Korea about restarting nuclear talks, we are delighted to have as our special guest today, the secretary of state, Condoleezza Rice (search), who's on a trip to the Middle East. We talked with her earlier in Jerusalem.

(BEGIN VIDEOTAPE)

WALLACE: Secretary Rice, welcome back to "FOX News Sunday."

New polls show growing doubts among Americans about the U.S. involvement in Iraq, and I'd like to take a look at the numbers with you if I can.

In the latest Gallup poll, 56 percent of those surveyed say they no longer think it was worth going to war in Iraq. And 59 percent say the U.S. should now withdraw some or all of our troops.

And then this week, a small group of Republican and Democratic congressmen called for troop withdrawal starting next year.

Can the Bush administration fairly be criticized for failing to level with the American people about how long and difficult this commitment will be?

SECRETARY OF STATE CONDOLEEZZA RICE: The most important point about Iraq is that it was time to deal with Saddam Hussein and to create conditions in this very important region, this very volatile region, that would help bring about a different kind of Middle East so that the United States can be secure.

The Middle East came home to us on September 11 in ways that we never expected. And without change in this region, we're going to continue to fight terrorists for a very, very long time.

Now, we have a different kind of Iraq. It is still a young Iraq, a young, democratic Iraq.

But if you look at the progress that they have made on the political front -- the turnover of sovereignty, the creation of a transitional administrative law, elections in January of this year, a constitutional committee now to write a constitution, and they will have elections in December -- they've made very rapid progress.

And so the administration, I think, has said to the American people that it is a generational commitment to Iraq. But it is not a generational commitment in military terms; it is a commitment of our support to them, our political support and an understanding that democracy takes time. But they're making very rapid progress.

In terms of the security situation, yes, there are a few terrorists and so-called insurgents who are plying their wares in a way that gets a lot of attention. They can create a lot of havoc, wreak a lot of havoc, create carnage against innocent Iraqis and against the coalition.

But they in time are going to realize, I think they may already realize, that as this political process goes forward, as more and more Iraqis are involved every day in the politics, they are the outliers. They're the ones who are keeping the Iraqis from doing what they wish to do.

And just one other point, Chris: The security forces of Iraq are getting better. We're making progress, making steady progress. They're not yet ready but they are taking over every day more and more of what the coalition has done. And that will mean that there is less need for coalition forces.

We are having success against the Zarqawi network, having picked up one of his key lieutenants just the other day. So I would say to the American people: Yes, this is very hard and very difficult. But we are making a lot of progress on what is going to be a strategic breakthrough for the United States, which is to have a different kind of Middle East.

WALLACE: Secretary Rice, I want to continue to explore this question of why there seems to be growing unease in this country about our commitment and the issue of leveling with the American people.

Here is what Vice President Cheney said recently about the insurgency. And let's take a look: "I think we may well have some kind of presence there over a period of time. But I think the level of activity that we see today from a military standpoint I think will clearly decline. I think they're in the last throes, if you will, of the insurgency."

What hard evidence do you have that the insurgency is in its last throes?

RICE: Well, there's no doubt that the military activity in which we will have to engage will decline. Just to give you an example, we did not have to get involved really in protection of the elections. These efforts that we're making up on the Syrian border are joint efforts with Iraqi forces. And they are doing much of the work in and around Baghdad on their own with just some logistical support.

So our military effort will decline.

Now, in terms of the nature of the insurgency, insurgencies are defeated not just militarily, they're defeated politically. And the Iraqi people are engaged in a political process in which more and more Iraqis see their future as a political future in a united and democratic Iraq.

As they held elections, as they are writing a constitution, as they will hold elections again, Iraqis see where their future is.

They're going to continue to suffer, I'm afraid, for some time from these insurgents and terrorists who wish to just kill innocent Iraqis because they have no other alternative. But that does not mean that they are going to win the battle for Iraq because that is being won by the Iraqi people on the political front.

WALLACE: But, Secretary Rice, let's look at the hard numbers about the insurgency from Iraq, and let's put them up. There were 70 attacks a day in May. That's the highest level so far this year. The number of U.S. troops being killed this year was the highest in May and June. And so was the number of Iraqi military and police fatalities.

Does that show an insurgency that, as the vice president says, is in its last throes?

RICE: First of all, obviously any loss of life, American or Iraqi, is to be mourned. The fact is, though, that you have to look not just at what the insurgency is doing and the carnage that they're creating.

It's the kind of thing where suicide bombers or an improvised explosive device can cause a lot of carnage without, frankly, many people having been engaged in it. That's the way these terrorists and insurgents work.

But you don't look just at what is happening on the security side; you also have to look at what is happening on the political side. And Iraqis, including Sunnis who really didn't see their future as being engaged by the political process, are now seeing their future as engaged by that political process.

I am told by our military people and by our intelligence people that we're getting more and more intelligence tips from Iraqis because they don't want these terrorists and these so-called insurgents to blow up their children standing at a school. They don't want these so-called insurgents and terrorists to blow up the brave men and women who are volunteering for the Iraqi armed forces and for the Iraqi police. The Iraqi people are not supportive of these insurgents.

Yes, they can continue to cause carnage. But what they're losing is that they're losing the Iraqi people. And that's the most important loss that you can inflict upon an insurgency.

WALLACE: Secretary Rice, let's turn to Iran (search). There's going to be a run-off there next week between the two top finishers. I know that you and President Bush believe that this was not a fair election. But one of the two people in the run-off, in fact the leading finisher, former President Rafsanjani (search), has campaigned on trying to improve relations with the U.S. He is going to be opposed by the hard-line mayor of Tehran.

Does it make any difference who wins that election?

RICE: Well, we've always said that the question here is the behavior of the Iranian government, the unelected few who are determined to frustrate the democratic hopes of their people, Iran's support for terrorism.

I'm sitting here in Jerusalem. I've been in discussions with Palestinian Authority (search) leaders and with the Israeli leaders, and they have a common concern.

And their common concern is for the terrorists, the rejectionist terrorist groups that could frustrate the desire of the Palestinians and the Israelis to live in peace. We're about to go through a very important step here with the disengagement. And a group like the Palestinian-Islamic Jihad that just announced that it's not going to live up to the agreement that it had with the Palestinian Authority to provide calm -- who's one of their biggest supporters? The Iranians.

So the Iranians are out of step with this region and that's what we hear about. As to the mechanics of their election, well, I think like any election in which thousands of people are disqualified by fiat and in which women are disqualified as a class barely deserves to be given that title, particularly in a place that several years ago seemed to be moving in a different direction.

WALLACE: North Korean leader Kim Jong-Il (search) now says that his nation is ready to resume nuclear talks perhaps as early as next month if -- repeat, if -- the U.S. treats his country with respect. Now, the North Koreans apparently were impressed that President Bush recently called him "Mr. Kim," but they were outraged when you called North Korea an outpost of tyranny.

Accurate or not, is it time cool the rhetoric to try to get these talks going again?

RICE: The North Koreans love to make excuses for why they can't come to the six-party talks. The reason they don't want to come to the six-party talks is they don't like facing China and Russia and Japan and South Korea and the United States telling them in a concerted fashion that it's time to get rid of their weapons, their nuclear weapons. That's why they don't to want come to the six-party talks.

This doesn't have to do with what somebody's called or whether somebody states facts about the North Korean regime. This is because the North Koreans want to avoid the inevitable confrontation, in a sense, with those who do not believe that the North Koreans can have nuclear weapons and that you can have a secure and peaceful Korean Peninsula.

(CROSSTALK)

WALLACE: So do you stand by the appellation that it's an outpost of tyranny?

RICE: Chris, I think the nature of the North Korean regime is self-evident. And everybody knows the nature of the North Korean regime. The point is that the North Koreans have been told by their neighbors and by the international community that the only way that they gain the respect that they say that they want, the only way that they gain some help with their terrible economic situation is to make a strategic choice to give up their nuclear weapons and come back to the six-party talks.

We even went to the New York channel to once again communicate the message to them about what would be available to them in these talks. So they have plenty of evidence, plenty of information on which to base their decision. And when they're ready to set the date, we're ready to listen.

WALLACE: We only have a couple minutes left and so I'd like to do a lightning round with you, if I could, Secretary Rice: quick questions, quick answers.

It appears that Senate Democrats are going to keep holding up the nomination of John Bolton to be U.N. ambassador. You say that it's very important to get him on the job so that you can continue the reform movement at the U.N.

Why not make a recess appointment to get him there to the U.N. as the ambassador?

RICE: Well, we just want to see what's going to -- we'll see what happens this week. The Senate should vote up or down. And the administration has answered countless questions. John Bolton has answered countless questions. Senator Roberts has responded to the issue of what kinds of information John Bolton was seeking from intelligence sources. Let's get the vote done.

WALLACE: The Democrats' number-two man in the Senate, Dick Durbin, created quite a stir this week when he compared U.S. treatment of prisoners at Guantanamo to Nazi Germany, Stalinist Russia and the killing fields of Cambodia.

Does it make it harder for you to do your job as you travel through the Mideast and push U.S. policy on human rights and democracy when a top American official says we're part of the problem?

RICE: Well, we're going to continue to talk about what the United States is doing positively for the people of this region. I'm here, the Iraqi people are voting, the Lebanese people at least are free of Syrian military forces.

And, in fact, we are a country that believes in international law, that believes in living up to our international obligations, including at Guantanamo, where the president made very clear that that was what would govern our efforts and our behavior at Guantanamo.

And I think it's quite clear that the United States simply doesn't fit into any of the categories that were said there. I'm a Soviet specialist; I know what the Soviet gulag was like.

WALLACE: Do you have anything specific to say about Senator Durbin's remarks?

RICE: As I said, I was a Soviet specialist. I think I know what the gulag was like. I think people know what the Cambodian killing fields were like. And I think people know what Nazi Germany did to 6 million Jews. And I think to say that the comparisons are not apt is to understate the case considerably.

WALLACE: And finally, I know that you have ruled out running for president in 2008. But I want to ask you about that. Is there something about running for office that is unappealing to you, that either you don't like or think you wouldn't be good at?

RICE: I've just never wanted to do it, Chris. I didn't run for class president any time that I can remember. I like what I'm doing. And this is a time when I think I've got a chance to help this president make a difference, to help the United States in this moment of American influence to make a difference. And so I'll keep after that.

WALLACE: Secretary Rice, we want to thank you so much for talking with us. Safe travels. And we hope to see you again here soon in Washington.

Up next, what needs to be done to fix the U.N.? A powerhouse political odd couple after this break.