[Brian Todd, Cnn Correspondent:] And it's not clear how much control he has Wolf.
[Wolf Blitzer, Cnn Anchor:] Fascinating, fascinating information. Brian, thanks for that report. And you're in THE SITUATION ROOM. Happening now: Cars and people crowd the streets of Gaza to celebrate the new cease-fire between Israel and Hamas, but how long will it hold? I will ask a Hamas spokesman what he expects in the hours and days ahead. And a reminder that many Israelis are still in danger. A public bus in Tel Aviv bombed just hours before the truce was announced. I will ask the Israeli prime the Israeli president, I should say, Shimon Peres, if a cease-fire might give Hamas more influence in the region. Stand by for our interview at this historic moment in the Middle East. We want to welcome our viewers in the United States and around the world. I'm Wolf Blitzer in Jerusalem. You're in THE SITUATION ROOM. We're keeping a close watch on the situation in Gaza right now as well as the situation in Southern Israel four hours into the cease- fire between Israel and Hamas. Here's a look at the situation in Gaza first. People have been celebrating the truce agreement, a break in Israel's deadly eight-day air offensive against Hamas. Israeli Prime Minister Benjamin Netanyahu says he's trying to give the cease-fire a chance, though Israel says militants in Gaza have fired at least five rockets since it went into effect. Netanyahu warns a ground war of Gaza is still an option if if the truce fails.
[Benjamin Netanyahu, Israeli Prime Minister:] I know there are those who expect an even more intense military response, and that may perhaps be needed. But at this time, the right thing for the state of Israel is to exhaust this opportunity to obtain a long-term cease-fire or an ongoing cease-fire. As the prime minister, I have the supreme responsibility to take the right steps to safeguard our security. That is what I have always done and that is what I will continue to do.
[Blitzer:] The cease-fire was announced by Egypt's foreign minister and the visiting Secretary of State Hillary Clinton in Cairo. Both Egypt and the U.S. played critical roles in these negotiations. The agreement was reached despite the bombing of a public bus in Tel Aviv earlier in the day; 24 people were injured. No one was killed. Western leaders strongly condemned it as a terrorist attack. I have been talking to top Israeli officials about the cease- fire. Now let's get the Hamas point of view. We're joined on the phone by the Hamas spokesman Osama Hamdan. He's in Beirut. Mr. Hamdan, thanks once for joining us. You joined us yesterday before there was an agreement. Is Hamas now prepared to stop all shelling of rockets, missiles, firepower into Israel?
[Osama Hamdan, Hamas Spokesman:] Well, thank you very much for this question. In fact, we have agreed on
[Blitzer:] So there's no more shelling, no more rockets going into Israel. What other commitments were you asked to make by the Egyptians, who acted as the mediator?
[Hamdan:] Well, in fact, if the Israelis continue fulfilling their commitments, respecting what they have agreed on, not attacking Gaza, lifting the siege
[Blitzer:] Have you made a commitment it's a little unclear to me to stop some of these weapons, the rockets that have been smuggled into Gaza through those tunnels, especially missiles coming in from Iran?
[Hamdan:] Well, I think the commitments are clear, the commitments of both sides are not going to attack the other side through the borders. And that's clear. If you want to talk about other commitments, I think this is something to be negotiated another time. This time, we have negotiated the cease-fire. And those were the commitments, no attacks, both sides, opening the crossing border, lifting the siege. That's it. So if anyone is asking about any other commitments, we didn't negotiate that. No one has negotiated this. If that was on the table, to clear, there is a statement in the agreement if there is anything to be discussed, it's supposed to be put on the table and discussed later on. So we did not discuss the points which you have mentioned.
[Blitzer:] We heard from a spokeswoman for the Israeli military say that there were five what she described as relatively minor incidents, rockets coming in, since the agreement went into effect. But I want to make it clear, does Hamas completely control all of Gaza, or are there other splinter groups that might be launching some of those rockets that Hamas perhaps doesn't necessarily control?
[Hamdan:] Well, in fact, the movements who participated in the negotiations or
[Blitzer:] There was a terrorist bombing of a bus in Tel Aviv today; 24 Israelis were injured. No one was killed. I know that Hamas issued a statement earlier praising this, although denying any responsibility. What, if any, role did Hamas perhaps have to play in this incident in Tel Aviv?
[Hamdan:] Well, as you have mentioned, someone else proclaimed the responsibility of this operation. We are in the situation that the Israelis are bombing us and the Palestinians are resisting that. Now we are in a different situation. And according to this new situation, we have to see if anything has been part of the agreement or not. And I think that asking such questions will not be useful, because the agreement was clear. And we are saying more also clear we will not break down or violate this agreement. If someone else who was not part of that violated that, I think that will bring the blame on him, not on any other parties.
[Blitzer:] One final question, Mr. Hamdan, before I let you go. If the cease-fire holds over the next several weeks, do you hope it will lead perhaps to real peace negotiations between the Palestinians and Israelis, leading towards what is called a two-state solution, Israel alongside Palestine?
[Hamdan:] Well, I hope that cease-fire can maintain itself and we can maintain it for the needed time in order to make real change in the situation. In fact, the Palestinian people are looking forward to have their rights and to achieve their goals of creating their independent sovereign state. And they are trying to and they are hoping to do that and the minimum rights which is supposed to be big. And I assure you, if they can do that by the help of the international community more easier, they will do it. But at the same time, they are ready to resist, to fight, to strike
[Blitzer:] Osama Hamdan is a spokesman for Hamas. Mr. Hamdan, once again, thank you for joining us. Let's hope this agreement, the cease-fire works and eventually this peace process can get back off the ground. Appreciate it very much. The White House is making it clear that President Obama strongly encouraged the Israeli prime minister to agree to the cease-fire. In fact, they have just released these photos of the president on the phone with the prime minister, Benjamin Netanyahu, the Egyptian president, Mohammed Morsi, as well as a picture of him talking to Secretary of State Hillary Clinton about sending her to the Middle East. Let's bring in our foreign affairs correspondent, Jill Dougherty. She's over at the White House watching this story for us. Jill, you have learned more about the president's direct role behind the scenes. What are you picking up?
[Jill Dougherty, Cnn Foreign Affairs Correspondent:] Yes. Wolf, the White House of course is praising Secretary Clinton, saying she did exceptional work on or all of this. But they are also making it clear that the president, as one senior official told me, was involved in this shuttle diplomacy, not actually physically, of course, the way Secretary Clinton was, but certainly with those phone calls, as you pointed out. In fact, this official said that it was really the last two phone calls that the president made, he would argue, that clinched the deal, that made the difference. And those were the phone calls to Israeli Prime Minister Benjamin Netanyahu and also to the Egyptian president, Morsi. They also point out they gave some background details that during this trip, even though we were initially told that the president was being briefed by Secretary Clinton and his national security adviser, we're told now that he was on the phone a lot, of course, almost every day, as one official put it, to Benjamin Netanyahu, a lot of conversations, three in fact in the last 24 hours, with President Morsi. And that Morsi relationship is of course very important. It's a burgeoning relationship and they say based a lot on trust.
[Blitzer:] Certainly is. Beyond the cease-fire, which is critically important people are going to stop dying if this cease-fire holds what about each side? What else did they gain?
[Dougherty:] I think starting with Israel, you would have to say they got the agreement to help stop getting allowing those weapons into Gaza, especially the weapons that come from Iran, and then also the extra money pushing for extra funding for Iron Dome, which has saved a lot of lives, and other systems. Then if you looked at let's say the Egyptians, I think this role that White House is stressing a lot, the relationship with Morsi, his personal role, Morsi's personal role, is going to be very important in the future. There was a lot of criticism of Egypt on Capitol Hill. That could help to salvage money certainly. And then also for Hamas, you would have to say not targeting individuals, that would be very important for Hamas Wolf.
[Blitzer:] Very important, indeed. Jill Dougherty at the White House for us, thanks very much. For the first time in several years, there's been a major terrorist attack in Tel Aviv. We're going live with the latest on the bus explosion right in the heart of the Israeli commercial center. Plus, my interview with the Israeli president, Shimon Peres, and his take on the idea of making the former U.S. President Bill Clinton the next special envoy for the Middle East.
[Shimon Peres, Israeli President:] I have the highest regard for President Clinton. I think he's an outstanding person. He's the most sunny president I can think of.