The following is a rush transcript of the May 30, 2010, edition of "Fox News Sunday With Chris Wallace." This copy may not be in its final form and may be updated.

CHRIS WALLACE, ANCHOR: On this Memorial Day weekend, we are honored to talk with America's top military man, Admiral Mike Mullen, chairman of the Joint Chiefs of Staff.

And, Admiral, welcome back to "Fox News Sunday."


WALLACE: Let's start with North Korea. How serious is the risk of armed conflict on the Korean peninsula? And how is it that North Korea can sink a South Korean warship, killing 46 sailors, without a military response?

MULLEN: Well, it's a part of the world that we're always very focused on in terms of sustaining stability. And the goal remains to certainly not have a conflict break out. That said, North Koreans committed, you know, a heinous act, if you will. Forty-six sailors in South Korea were killed.

And we've been working with South Korea, a very strong ally, in support of them in terms of moving forward here. So there's always risk. And I'm concerned there's — with Kim Jong-Il. It's — he always — he just doesn't seem to do single things. So I'm concerned that, you know, there could be follow-on activities.

That said, I think certainly the political and diplomatic and international focus to keep it stable in that part of the world is absolutely vital.

WALLACE: Do you think that that stability is more in question, more at risk, than it usually is?

MULLEN: Well, certainly, after an incident like this, stability is something that we focus on, and it becomes more fragile. There's — there are also issues in North Korea tied to his succession.

So there's a great deal of focus on this right now in terms of keeping it stable and responding appropriately from an international standpoint.

WALLACE: There's a new U.N. report that North Korea has been secretly exporting — smuggling — nuclear and missile technology to other parts of the world, including Syria and Iran. Should the U.S. put North Korea back on the list of countries that sponsor terrorism?

MULLEN: Well, not — certainly not for me to decide. That's really a decision for President Obama and the leadership, the political leadership, in our country.

That said, North Korea is a known proliferator, as you've suggested. I haven't seen the report so I couldn't speak to the details of it. And that proliferation is something that we would — we really would like to see stop. It creates a danger, and it was something that was addressed in the most recent United Nations Security Council resolution against North Korea. I think it was 1874, the last time that North Korea acted up. And we need to keep that focus.

WALLACE: Let's turn to the rogue regime in Iran. We still don't have, after months of talk, a new set of sanctions against Iran. Most experts doubt that whatever we end up getting from the U.N. is going to stop Iran from pursuing its nuclear ambitions.

You have talked on this show the last time you were on about how destabilizing a U.S. military strike would be. Have you thought about what it will take to contain a nuclear Iran?

MULLEN: Well, first of all, there is continued focus on the sanctions. I'm hopeful that those which have been preliminarily approved in New York actually get put into effect. I think it's very important in that regard because of the ability or the legitimacy in terms of moving forward and continuing to isolate Iran, as Iran continues to isolate itself.

That said, the destabilizing impact of them achieving weapons capability, along with the destabilizing impact of striking them from whomever it came, is something I continue to be extremely concerned about. I also...

WALLACE: So if I may, if we ended up, despite our best efforts, with a nuclear Iran, what would containment look like?

MULLEN: That's a hypothetical at this point. Certainly, it's something that is of...

WALLACE: Not very hypothetical.

MULLEN: Well, it's a longer-term concern. And when we — if for some reason we ever got to that position, then I think we'd address that issue. I haven't spent a great deal of time on that up to this point.

WALLACE: In Afghanistan, we keep hearing that we're going to have soon a major offensive in Kandahar. On the other hand, you say this is not going to be a D-Day operation. Do you expect the Taliban to make a stand in Kandahar? And how central is the battle of Kandahar to victory in Afghanistan?

MULLEN: I've said for many months I think the violence level is clearly going to go up this year. It has already in Afghanistan. And Kandahar is central to that. In our focus on Kandahar we've initially started to shape that operation. And it is central to the long-term outcome.

I think Kandahar will give us very clear evidence of how this strategy is proceeding. It is the home of the Pashtun resistance. It's the — it is the — it is central to the insurgency. So I think success in Kandahar over the next many months is absolutely critical to the longer-term outcome in Afghanistan.

WALLACE: There's a report out this weekend that the Pentagon is reviewing plans for a major strike in Pakistan if, God forbid, there should be a successful terror attack here on the U.S. homeland and it can be traced back to Pakistan.

Question: Are you putting terror groups and the Pakistani government on notice?

MULLEN: I've spent an extraordinary amount of time in Pakistan in dealing with my counterpart there, General Kayani, and I've been impressed with how much Pakistan has evolved over the last couple years. They've lost a significant number of troops. They've regained a significant amount of their territory. They're very focused on that.

They're struggling in building behind the security that they've created, in — particularly in the western area. They've moved some 70,000 troops to the west. So we're working hard to strengthen that relationship. We're working hard to support them in training. And we'll continue to do that.

WALLACE: But when you talk about a unilateral strike if there's a successful terror attack, are you putting the government and the terror groups on notice we'll take this into our own hands if need be?

MULLEN: Well, again, my focus, more than anything else, is in support of them. And clearly, I mean, we're very concerned about that part of the world. We're very concerned about — that's where Al Qaida leadership lives. We know that. And we're working with Pakistan and, quite frankly, with Afghanistan to continue to put pressure on that leadership.

And I wouldn't speak to any kind of details in terms of either plans or operations.

WALLACE: The full House and a Senate committee voted this week to repeal "don't ask, don't tell," even though the Pentagon review won't be completed until the end of the year.

Does that send the wrong message to our troops when the House and a major committee in the Senate are, in effect, saying, "We've already decided what we're going to do before we hear from you?"

MULLEN: Well, I said in my testimony in February that personally I believe that the law is — that the law should change. But I also said that this review was critically important.

Ideally, I would like the legislation to wait until we've completed the review so we can look at how to implement it when the legislation goes...

WALLACE: But does it send the wrong signal to the troops if they see the House already passed the repeal?

MULLEN: Well, we've worked hard so far in this review to understand what's going on with respect to our troops. And I don't control the legislative calendar. And the other thing is recognizing the votes that took place, I certainly understand that.

But it's — there — I think it could be many months before this thing — before the legislation actually was finally completed and it was passed.

WALLACE: Let me ask you another aspect of that. The House passed the repeal as an amendment to the Defense Authorization Act. And the Senate Republicans are saying if that's in the authorization act that — when it gets to the Senate floor that they'll filibuster it.

Do you worry that military spending could get all mixed up with social policy?

MULLEN: Actually, less a worry with respect to spending in support of our men and women, particularly those in the wars right now, than it is putting the — putting the force in the middle of this debate, which is something that we have sought from a leadership perspective to avoid. And by and large, so far that's been the case.

What I don't want to do is electrify the force at a time when they're going through two — in the time of two wars, the length of time that we've been at war. And when we get to a point — we get through the review, we'll understand what it takes to implement it.

And having time — and in fact, I, with the secretary of defense and the president, would certify that we're ready for implementation at the time that that really should take place.

WALLACE: Finally, Admiral — and we only have about a minute left, but we'd like to give it to you. Do you have a message both to our troops and to the rest of America on this Memorial Day weekend?

MULLEN: Well, I can't put — it's hard to put into words the feelings that I have in support of so many who have given so much over the course of our history, but particularly in these wars.

My wife and I spent time Friday with hundreds of members of families of the fallen — families of the fallen, and that their sacrifices never be forgotten, that their sacrifices continue to make a difference, not only in these conflicts and for people around the world, but in support of our national security interest and their bedrock to who we are as a country.

They are the best military I've ever been associated with. There's not a day go by I don't think about them, their sacrifices, the service and the difference that they make. And I'm very grateful for all of that.

WALLACE: Admiral Mullen, we want to thank you so much for coming in today, and we thank you and our forces...

MULLEN: Thank you, Chris.

WALLACE: ... around the world for all of your service, sir.

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