The following is a partial transcript of the July 20, 2o08, edition of "FOX News Sunday With Chris Wallace":

"FOX NEWS SUNDAY" HOST CHRIS WALLACE: Senator Barack Obama is on the ground in Afghanistan on day two of his high-profile trip to the Middle East and Europe.

The presumptive Democratic nominee met in Kabul today with Afghan president Karzai whose government he has sharply criticized. Earlier Obama talked with U.S. military officials and he had breakfast with the troops.

(BEGIN VIDEO CLIP)

OBAMA: (inaudible) see young people (inaudible) like this who are doing such excellent work, with so much dedication and drive (inaudible).

(END VIDEO CLIP)

WALLACE: Later, Obama is expected to fly to America's other war zone in Iraq.

Joining us now for his first Sunday show interview, Admiral Michael Mullen, chairman of the Joint Chiefs, who's recently back from his own trip to the region.

And, Admiral, welcome...

MULLEN: Good morning, Chris.

WALLACE: ... to "FOX News Sunday".

MULLEN: Thank you.

WALLACE: President Bush and Iraqi prime minister Maliki announced Friday that they have set what they call a time horizon for the transition to Iraqi command and further withdrawal of U.S. troops.

Now, they are saying that these would be goals, not deadlines, but what's your sense of how fast that transition might come?

MULLEN: Well, I think — I'm not yet able to put an exact time line on it per se. I think the strategic goals of having time horizons are ones that we all seek because eventually we would like to see U.S. forces draw down and eventually all come home.

And I think part of what I see going on is healthy negotiations for a burgeoning democracy, and I think these discussions are indicative of that.

WALLACE: Will this time horizon have a date, even if it's just a goal, for when U.S. combat troops would be out and the Iraqi military would have control of their own security?

MULLEN: This right now doesn't speak to either time lines or timetables, based on my understanding of where we are.

WALLACE: So what would the horizon say?

MULLEN: Well, I think it sends a signal that there is one, that eventually we do want to bring our troops back, and that — and right now that — with where we are, conditions are improving in Iraqi. Certainly, when I was there a week before last, that was indicative.

And if those conditions continue to improve, we should be in a position to start to bring our troops home.

WALLACE: Prime Minister Maliki was quoted in a German magazine this weekend saying he thinks that Senator Obama's plan to pull all U.S. combat troops out within two years, by 2010, is — and let's put it up on the screen — the right time frame for withdrawal.

His spokesman has now backed away from that a bit, so that any pullout is based on continuing progress on the ground. What do you think are the consequences if we set a time line for pulling all troops out within two years?

MULLEN: Well, my current mission under the current commander in chief is to give him advice and recommendations based on our progress there, and that's exclusively based on conditions on the ground, and that's the mission that I've got.

Should that mission change, and we get a new president, and should those conditions be conditions that get generated or required in order to advise a future president, I would do so accordingly.

Based on my time in and out of Iraq in recent months, I think the conditions-based assessments are the way to go and they're very solid. We're making progress, and we can move forward accordingly based on those conditions.

WALLACE: But I'm asking you in the absence — forget about Obama. Forget about the politics. If I were to say to you, "Let's set a time line of getting all of our combat troops out within two years," what do you think would be the consequences of setting that kind of a time line?

MULLEN: I think the consequences could be very dangerous in that regard. I'm convinced at this point in time that coming — making reductions based on conditions on the ground are very important.

We've been able to do that. We've reduced five brigades in the last several months. And again, if conditions continue to improve, I would look to be able to make recommendations to President Bush in the fall to continue those reductions.

WALLACE: Why dangerous to set a timetable now for what's going to happen over the next two years?

MULLEN: When I have discussions with commanders on the ground, basically — and I did a couple weeks ago — they are very, very adamant about continuing progress, about making decisions based on what's actually happening in the battle space, and I just think that's prudent.

That's served us very well in — certainly, since the surge, which has been very successful, and I think will continue to serve us well based on the overall conditions that I see in Iraq right now.

WALLACE: And why? What would happen if you don't do it as condition-based? What if you sit there and say, "Right now, timetable, two years, all combat troops out?" What's the downside?

MULLEN: Well, it's hard to say exactly what would happen. I'd worry about any kind of rapid movement out and creating instability where we have stability.

We're engaged very much right now with the Iraqi people. The Iraqi leadership is starting to generate the kind of political progress that we need to make. The economy is starting to move in the right direction. So all those things are moving in the right direction.

And from the standpoint of moving forward, I think it's a pretty good path right now.

WALLACE: Now, you, as we said, are just back from Iraq, and when you came back you said that security is so much better that you may well be able to recommend more troop cuts this fall.

Can you see more troops coming out of Iraq before President Bush leaves office?

MULLEN: If conditions on the ground continue to improve as they have, what I said the other day is what I believe, that I will — think I'll be able to make recommendations for the president to withdraw more troops.

There's a mechanical, physical challenge with respect to moving troops around. You can't just do it overnight. So those decisions have to be taken — those facts are taken into consideration in terms of making those decisions, and we're working through the details of that right now, and so I can't tell you for sure whether we could get more troops there before the end of the year or not.

WALLACE: You mean get more troops out.

MULLEN: Get more troops out.

WALLACE: Assuming this current glide path, which is, you feel, an improving glide path, is it your sense it would be possible to get more troops out before the president leaves office on January 20th?

MULLEN: You'd have to go through the assumptions, but certainly there are assumptions which you could make which would make that possible.

WALLACE: There's been talk about as many as three more combat brigades.

MULLEN: Again, I think that's pretty — you have to look at the assumptions very carefully about that in terms of whether we could do something like that.

WALLACE: While we're talking here, Senator Obama is either on his way or at least headed to Iraq. He opposed the troop surge, while Senator McCain was one of its earliest supporters.

Again, having said that, try to divorce it now from politics. You say you're surprised at how much security has improved from when you came on your trip, that you were surprised that it's so much better.

MULLEN: Sure.

WALLACE: What's your best estimate of where we would be if there had been no troop surge, and instead of adding the troops over the last 18 months we'd been pulling them out?

MULLEN: Well, hard to — that's a — actually, that's a hypothetical that I would struggle really answering. What I saw on this trip was — I had a certain mindset about improved security because I certainly knew it had.

And relative to where I thought it was, in fact, it was better, much better, than I had anticipated. And that has to do with walking around Sadr City and being in the Jamilla Market, which is a central market in Iraq, walking through Mosul, downtown Mosul, where a few weeks ago we couldn't go, what's happened in Basra, how we've made improvements there in terms of security, and also the confidence that the Iraqi security forces have, the Iraqi leadership has right now in terms of taking control of their own destiny.

And so all of those things came together for me to sort of culminate in an assessment that it was much better than I had anticipated.

WALLACE: Do you think that could have happened without the surge?

MULLEN: No, I don't think it could have.

WALLACE: Let's turn to Afghanistan. General Petraeus, still the commander of U.S. forces in Iraq but headed on to become central commander, says that Al Qaida may no longer consider Iraq the front line in the war on terror and may, in fact, be shifting some of its foreign fighters from Iraq to Afghanistan. Do you see that shift?

MULLEN: I think he also said that there's no firm evidence of that yet. In my trip there week before last, certainly the whole issue of the FATA and the safe havens for foreign fighters, for Al Qaida, for Taliban and the insurgents that are now freely — much more freely able to come across the borders — a big challenge for all of us.

And it's having an impact on our ability to move forward in Afghanistan. The concern, certainly, is that safe haven exists and that we — and when I say we, I think the international community...

WALLACE: We're talking about the safe haven between the Afghan- Pakistan border.

MULLEN: Right. Actually, it is a safe haven in Pakistan...

WALLACE: In Pakistan.

MULLEN: ... which is where these foreign fighters — some additional foreign fighters have shown up — not necessarily Al Qaida.

But what I do see in that part, particularly in the FATA in Pakistan, is a joining, a syndication, of various extremists and terrorist groups which provides for a much more intense threat, internal to Pakistan as well as the ability to flow — greater freedom to flow forces across that porous border.

WALLACE: Given what I'm hearing here and what I've heard in your statements since you returned, is it fair to say that we're now winning the war in Iraq and losing the war in Afghanistan?

MULLEN: I think we've made a lot of progress in Iraq, and certainly every indication is that we're proceeding in the right direction. I would not say in any way, shape or form that we're losing in Afghanistan. In fact...

WALLACE: But we can't say we're proceeding in the right direction.

MULLEN: The attacks, actually, that have been publicized recently — there was one, obviously, at Wanat which was a very serious attack — it was a very sophisticated attack, and we lost nine soldiers there, and my thoughts and prayers go out to the families of those who sacrificed so much there and really throughout these wars.

But when I visit with the commander up in Korengal Valley just in the same vicinity — I was there with him a couple of months ago. They've actually made progress and moved into small villages further in the valley.

When I visited with the Marines down south, which are an additive to our troops in Afghanistan, they've taken territory and held it and made a difference in ways that are very significant.

So I would say the progress is mixed there, but I am not concerned at all at this point that we're losing in Afghanistan.

WALLACE: Finally, let's turn to Iran. The news out of the nuclear talks in Geneva yesterday is that the Iranians refuse to say whether or not they will suspend their nuclear program, and the U.S. and our allies have given them two more weeks. Your reaction.

MULLEN: I'm encouraged by the talks. A few weeks ago I wouldn't have thought those were possible. And I believe that the international community needs to continue to bring pressure on Iran both economically, financially, diplomatically, politically, to continue to bring them to a point where we can all deal with this issue of nuclear weapons.

I fundamentally believe that they're on a path to achieve nuclear weapons some time in the future. I think that's a very destabilizing possibility in that part of the world. I don't need — we don't need any more instability in that part of the world.

So I was encouraged. I will obviously watch what happens in the next two weeks to see if they come further or if they walk away.

WALLACE: I want to ask you two questions about Iran. How do you weigh as a military man, as the top military man, the downside risk if either the U.S. or Israel were to militarily strike Iran in terms of blowback from Iran and its allies in the region, increased turmoil in that area, increased turmoil in the oil market?

MULLEN: I think it would be significant. I worry about it a lot. I've said when I've been asked this before right now I'm fighting two wars, and I don't need a third one to — I would be concerned — not that I couldn't — not that we don't have the reserve to do it in the United States. We do.

But I worry about the instability in that part of the world and, in fact, the possible unintended consequences of a strike like that and, in fact, having an impact throughout the region that would be difficult to both predict exactly what it would be and then the actions that we would have to take to contain it.

WALLACE: On the other hand, how do you weigh the downside risk of doing nothing?

MULLEN: There is significant concern with that as well. I mean, it's a very, very tough problem. But that's where I think this international community — and the pressure has got to continue to be brought specifically on Iran to not proceed in this regard.

And again, I believe they're headed in that direction.

WALLACE: Headed in the direction...

MULLEN: Headed in the direction of building nuclear weapons and having them in their arsenal, and that needs to — we need to figure out a way to ensure that that doesn't happen.

WALLACE: Admiral Mullen, we want to thank you. Thanks so much for coming in, and please come back, sir.

MULLEN: Thank you, Chris. It was good to be with you.