This is a partial transcript of "The Big Story With John Gibson," January 16, 2005, that has been edited for clarity.

JOHN GIBSON, HOST: Soon after the end of major combat in Iraq in May 2003, Ambassador Paul Bremer was assigned the tough job of overseeing the country's reconstruction until it was ready to be self-governed.

The former top U.S. administrator in Iraq recently wrote an op-ed in The New York Times about that experience, about some of the mistakes he made and why it would be a big mistake to pull our troops out too soon.

He's also the author of a new memoir about his time in Iraq. It is called "My Year in Iraq: The Struggle to Build a Future of Hope."

Ambassador L. Paul Bremer, "Jerry" Bremer, joins us now. So, Ambassador, one of the things that was in the news Monday that I thought you could comment on is an American official criticizing Saudi Arabia in this War on Terror and saying, "Look, the Saudis are letting these guys get into Iraq without even trying to stop them." Was that your experience as well?

PAUL BREMER, FORMER CPA ADMINISTRATOR: Well, we had a number of Saudis coming in. They tended to come in through Syria, actually, more than across the Saudi border, which is a very isolated desert area.

We did have one unit posted down on that border to try to keep them out. But I would say, I think it's important for all of Iraq's neighbors, I think mostly Syria and Iran, Saudi Arabia perhaps third, it's really important for them to stop making the situation worse there.

GIBSON: I take it you mean Syria? I think you talk about Syria in your book. And there's been a lot of discussion about Syria in the year or so that you've been back. What should the president do about Syria?

BREMER: You know, one of the most startling things that I learned and I write about it in the book is that the Syrian president, Bashar al-Assad, sent a message to Ayatollah Sistani, the leader of the Shia, in the fall of 2003 encouraging Sistani to issue a fatwa calling for an uprising of the Shia against the occupation against the American forces, which was really an act of incredible irresponsibility, which if Sistani had done, it would have cost American lives.

I think right now we have got some very useful pressure on the Syrian government as a result of their involvement in the assassination of the Lebanese prime minister. And we need to keep up that pressure. We have to get the Syrians to take better control of their borders. We've got to stop these underground railroads that are effectively bringing terrorists from Saudi Arabia, Yemen, Sudan, into Iraq across the Syrian border.

GIBSON: Ambassador Bremer, there has been a lot of discussion about bringing the troops home and there are some hopeful discussion that maybe in 2006, a sizable number of American troops will be able to leave Iraq. Is your opinion, from your time in Iraq, that we're in a less troops, not more troops situation?

BREMER: Well, I've been away now for a year-and-a-half so I'm a little reluctant to make comments on the exact numbers we should have, but I think the general principle is this: They should come home when we have actually succeeded.

We don't need a strategy for withdrawal. We need a strategy for victory. That's what the president's been talking about and he's right. To the extent that we defeat the insurgents and defeat the terrorists, then obviously we can bring our troops home.

The conditions on the ground where we are in fact winning the war, that will determine our troop strength, not some theoretical timetable.

GIBSON: Ambassador Bremer, a lot of people talk about these elections also. In this country, when they are trying to criticize the administration and what it's done, they've said, "Look at this election. Yes, there was election, and who won? The fundamentalists won."

Is that criticism true?

BREMER: Well, we actually don't know the final results. I think it will be the case that the Shia list, the United list, will be the biggest party in parliament. I don't think they'll have enough to run the place on their own. They are going to have to pay attention to the checks and balances, which we wrote into the Constitution. They are going to have to do what parliamentary democracies do, make a coalition.

And I'll tell you this, John. You know, I know these leaders, the Islamist leaders, the Shia leaders. I've spent hours and hours drinking tea with them all over the country. I don't think that they are on the way to trying to establish an Iranian type theocracy. They want a democratic Iraq and I think now it behooves them to try to pull together a government of national unity and I hope that's what we'll see here in the weeks ahead.

GIBSON: L. Paul Bremer, the book is called "My Year in Iraq: The Struggle to Build a Future of Hope." Mr. Bremer, it's always good to see you, thanks very much.

BREMER: Thanks.

Content and Programming Copyright 2006 FOX News Network, LLC. ALL RIGHTS RESERVED. Transcription Copyright 2006 Voxant, Inc. (www.voxant.com), 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, LLC'S and Voxant, Inc.'s copyrights or other proprietary rights or interests in the material. This is not a legal transcript for purposes of litigation.