This is a partial transcript from Your World with Neil Cavuto, April 29, 2003, that was edited for clarity. Click here for complete access to all of Neil Cavuto's CEO interviews.

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NEIL CAVUTO, HOST: Now reaction from the inside, we’re joined by Palestinian negotiator, Saeb Erekat.

Mr. Erekat, thanks for joining us.

SAEB EREKAT, PALESTINIAN NEGOTIATOR: Hi, Neil, how are you?

CAVUTO: I’m fine. What do you make of this call by some more militant members in Hamas that they’re not going to put down arms?

EREKAT: Well, that’s the real challenge. I believe that there is an opportunity for Israelis and Palestinians to re-engage in a meaningful peace process and talk to President Bush tonight to immediately introduce the road map, the means of implementation, the time line, the monitors. And once Palestinians begin to see the process of Israeli withdrawing, stopping their assassinations, stopping the settlements, I believe we can maintain the authority, and we can maintain a monopoly of arms only to the Palestinian security forces. It’s not going to be easy job, but this depends largely on the Americans and the other members of the Quartet introducing the road map immediately and without any further delay.

CAVUTO: But it also depends on some of the more militant groups, right? I want to read you a quote from a Hamas member who said, "Hamas will use its weapons against occupation only, and Hamas will fight this occupation until the full liberation." How do you feel about that?

EREKAT: Well, we don’t want parallel authorities. And every Palestinian party must understand that while we want to maintain the political pluralism, the freedom with opposition, there will be a red line.  There will be one authority and that is what we meant today in our government program. And that is what we mean by maintaining the oneness of the authority. But in order to be able to achieve that, we need the help of the Quartet committee to introduce immediate results.

CAVUTO: No offense, sir. It doesn’t look like you are going to get that help. Is there a fear here that this whole new authority has been set up to fail when some of the more militant groups are saying no?

EREKAT: No. I think the challenges are enormous, actually, whether it’s internal Palestinian complexities, or Israeli policies of settlement activities, the region, and the Iraq aftermath. But, as - tonight, as you heard the government program, there is a serious chance to revive the peace process. There is a serious chance to re-engage in a meaningful peace process. And what will make or break this effort is that once Palestinians and Israelis will see a meaningful peace process, that peace is doable, that there are partners on the other side, I believe the support of Palestinians and Israelis will make it happen. And that is the most essential ingredient in this process.

CAVUTO: If one Israeli is killed in a bus bombing, a disco attack, anything like that, the Israelis are apparently making it clear all bets are off. Do you agree? Do you agree with their position?

EREKAT: You know, look. I think at the end of the day the job of peacemaker is to save lives of Palestinians and Israelis. And in order to engage in saving lives of Palestinians and Israelis we must adhere to the work that the Americans and other members of Quartet have done in the road map. And we need to accept the road map and we need to begin seriously helping each other in implementing our obligations of the road map. At the end of the day we want to save lives of Israelis and Palestinians.

CAVUTO: Saeb Erekat, Palestinian negotiator, thank you very much.

All right. Reaction now from former Israeli Prime Minister Ehud Barak. What did you think?

EHUD BARAK, FMR. ISRAELI PRIME MINISTER: I think that the development of the approval is it is a positive development in the right direction, but the proof of the pudding is in the eating. We still have to see that they really deprive Mr. Arafat from any executive role as long as he.

CAVUTO: Yes. But did you see reception for Arafat today? It was pretty good.

BARAK: Reception is OK. But as long as Mr. Arafat will retain any concrete executive role, or influence there will be no peace. He behaved like a terrorist, looked like a terrorist and maybe he is a terrorist.

CAVUTO: But he is a terrorist working with this Mahmoud Abbas, who is now saying effectively, look, we have got to stop violence. I want to quote from him, Mr. Prime Minister. He says, "we denounce terrorism by any party and in all its forms because we are convinced that such methods do not lend support to a just cause like ours, but rather destroy it." Do you believe him when he says that?

BARAK: I give him the benefit of the doubt. And I prefer to be optimistic. But I can tell you in advance that the proof of this should be in the action, in deeds, not just in saying. And we will have to see Abu Mazen, Mahmoud Abbas in the land really cracking on Hamas, Islamic Jihad as well as Arafat’s own brigades of Al Aqsa.  If they will do that, they will deserve backing and support by the Americans, and gestures of good will by Israeli.

CAVUTO: But you have to make some concessions, that is Israel. And one of the key ingredients of this peace plan, or whatever you want to call it, is simultaneous moves. That is, Israel pulling out of camps, of settlements, and at the same time, the Palestinians, or the more severe members, stopping any terrorist campaigns. Would you think at this point Israel would agree to that?

BARAK: Certain, simultaneous step of gesture in nature like finding a way to ease the daily life of Palestinians or to impose rule of law on settlers or dismantle illegal outposts, that is something that Sharon’s government will have to do combined.

CAVUTO: Will it do it?

BARAK: Yes, I believe.

CAVUTO: But all bets are off, right? I don’t mean to keep interrupting, but all bets are off, aren’t they, Mr. Prime Minister? if there is a bombing or a terrorist attack, even though it might be conducted by a fringe group whose goal precisely to stop this peace process?

BARAK: I believe that both sides are clever enough not to let it explode just as a result of a single event or undisciplined player.

CAVUTO: But that is what happens.

BARAK: Once the road map will be launched, I believe it will be given for a short, limited time, an opportunity, backed by American backing to Abu Mazen and Israeli readiness to carry out certain gestures. But when the time comes for major steps to be made it could not be simultaneous. There is a need to see for sure that Arafat is removed from power.

CAVUTO: But he is not going anywhere, you know?  He might be sort of like a titular chairman in this country.

BARAK: It is a part of President Bush’s vision, and in a way, even of the road map, that this government of Abu Mazen will get every aspect of executive authority.

CAVUTO: But Mr. Barak, here is my point: Obviously there was a great reception, as Jennifer Griffin pointed out today, for Arafat. I know you don’t flip over the guy. The president of the United States doesn’t flip over the guy. But right now at least judging by that crowd today, he is still the guy. Do you worry that he is still going to call the shots?

BARAK: I have a clear observation that if he has executive role, rather than popular support and symbolic role, there will be no peace. He has already proven his capacity to destroy and miss every opportunity for peace. But at the same time there is a role for Abu Mazen, the new prime minister, in this land. And this is to be ready, to do it even against violent resistance by the Hamas and Islamic Jihad and to crack them, for the Palestinian reason not just for Israel, and put an eventual end to terror. If they fail to do that, no reason to ask Israelis to make any concessions as a down payment. If they are successful in doing this, I believe that it is a real turning point, where we will be able ultimately to achieve a peace agreement based on the principles of Camp David.

CAVUTO: All right. Ehud Barak, former prime minister of the state of Israel, good seeing you again. Thank you very much.

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