The IDF was ordered Monday night to prepare plans to target Palestinian terror organizations and Islamic Jihad terror chiefs in the Gaza Strip as a response to a suicide attack earlier in the day that killed three people in Eilat. The IDF also immediately reinforced troops along the border with Egypt, which security officials said the bomber used to infiltrate Israel. "We will not cut terror groups any slack, and the cease-fire will not prevent us from targeting them," Defense Minister Amir Peretz said following a security assessment with senior defense officials, including IDF Chief of General Staff Lt.-Gen. Dan Halutz. During the meeting, Peretz called for an end to the government's policy of restraint, claiming that it was time to strike back at Palestinian terror infrastructure in the Gaza Strip with the IDF's full force, but other government officials said it was first necessary to establish convincingly where the suicide bomber came from, and which organization was behind the attack. Prime Minister Ehud Olmert is set to hold talks Tuesday with Peretz and security officials to discuss the Eilat bombing and Israel's response. In the first suicide attack in Israel's popular southern resort town, a suicide bomber, identified as Islamic Jihad operative Muhammad Faisal Saksak, 21, of Gaza City, blew himself up at a bakery in a shopping center in Eilat's Ha'arava neighborhood killing three. Only one of them had been identified at press time: Yisrael Samoliya, 26, an immigrant from Peru whose family lives in Miami. He had been working at the bakery for about three months. Defense officials said Saksak infiltrated Israel across the 220 km. border with Egypt that is mostly fenceless and patrolled by minimal IDF and Border Police forces. Saksak is believed to have entered Egypt - possibly through an underground tunnel across the Philadelphi Corridor - and then was driven to the Egyptian border with Israel, which he crossed by foot some 30 km. from Eilat. From there he made his way to Eilat. According to a top officer in the Southern Command, the suicide attack was expected and was a threat for which the IDF was preparing. He predicted, however, that the success would motivate additional terror groups to try and send additional bombers into Israel. In 2006, over 100 Palestinian terrorists who originated in Gaza were caught trying to infiltrate Israel from Egypt. According to the officer, Israel also needs to demand that the Egyptians do more to prevent the infiltration of Palestinian terrorists into the Sinai and then into Israel. "The threat has not fully materialized itself yet even with this suicide attack," the officer said. "I am concerned that this is just the beginning and the attacks will continue to happen." Internal Security Minister Avi Dichter said the attack in Eilat was "an exceptional event" and one that the defense establishment planned to keep that way. "The entrance of the terrorist demands steps be taken with the Egyptians in order to ensure that the border remains a peaceful one," he said. Witnesses said the bomber stood out because he was wearing a long winter coat on a warm, sunny day when he struck the small bakery in a residential neighborhood. Police said the bomb was in a bag he was carrying rather than an explosives belt often used in past suicide attacks. Shattered glass, body parts and blood-splattered pastries were visible on the sidewalk outside, alongside bread trays scattered by the blast. Fawzi Barhoum, a Hamas spokesman in Gaza, called Monday's attack a "natural response" to Israeli military policies in the West Bank and Gaza Strip, as well as its ongoing boycott of the Hamas-led Palestinian government. "So long as there is occupation, resistance is legitimate," he said. He also said attacks on Israel were preferable to the recent bout of Palestinian infighting in Gaza between his group and the more moderate Fatah party of Palestinian Authority Chairman Mahmoud Abbas. "The right thing is for Fatah weapons to be directed toward the occupation, not toward Hamas," Barhoum said. Islamic Jihad, which claimed responsibility for the attack together with two other groups, posted a statement on its Web site Monday saying that it had engineered the bombing in an attempt to "focus Palestinians' attention away from killing each other." The only attack to hit Eilat since the outbreak of Israel-Palestinian violence in 2000 came in 2005, when terrorists linked to al-Qaida fired a Katyusha rocket from Jordan at the city, causing no casualties. The last deadly attack in the city was in May 1992, when Palestinian militants swam to an Eilat beach and killed a security guard. Prime Minister Ehud Olmert said in a Kadima faction meeting that for "a long time, Israel [had] enjoyed the illusion of quiet." Olmert said that in recent months, Israel had prevented numerous terror attacks. The prime minister said he would consult security officials, and only after all relevant intelligence had been collected would the IDF decide on a course of action. The IDF has asked for the erection of an electronic fence along the Israeli-Egyptian border, but due to the cost - NIS 1.5 billion - the money has yet to be transferred. At the moment, some five battalions patrol the border. Funds that were meant to be transferred to the fence were diverted to other projects as a result of the Lebanon war this past summer. Less than 15 minutes before the deadly bombing, police received a call from Lt.-Col. (res.) Yossi Voltinsky, alerting local security teams that he had just transported a hitchhiker who aroused his suspicions. Voltinsky said he had only understood that the man was suspicious after he had allowed him to enter his vehicle, and that the man had fled the car before he could lock him inside. Two police patrol cars arrived in the neighborhood within seven minutes of Voltinsky's car and began looking for the mysterious hitchhiker, but their efforts were cut off minutes later by the blast. Police suspect that the bomber proceeded on foot from the car to the nearest center of population, Eilat's Ha'arava neighborhood. There, he came to the small local shopping center known as Isadore, entered the bakery and detonated. "It seems that the terrorist came on foot, heard the police cruisers, became stressed and detonated himself. That is a definite possibility," said Southern District Police Chief Cmdr. Uri Bar-Lev. Video footage from a surveillance camera in a neighboring felafel shop seems to show the bomber, wearing a red shirt and carrying a black bag, passing by the store's window. Seconds later, the camera recorded the explosion, as the back wall of the felafel shop was blown apart by the force of the blast. The bakery's two young owners and one employee were alone in the bakery when the bomber walked in, and all three were killed immediately in the blast. Robert Tolesco, Magen David Adom's Eilat commander, said that when paramedics arrived on the scene they found no one in need of medical attention. Three people arrived at Yoseftal Hospital in Eilat following the bombing and were treated for shock. Bomb experts said the explosive weighed less than 10 kilograms, and that it appeared to be somewhat different from bombs detonated in earlier attacks. Even after receiving the warning, it still took police almost an hour to confirm that the explosion had been caused by a bomb and not a technical fault or a gas leak. After the bombing, Eilat Police Chief Asst.-Cmdr. Bruno Stein deployed police at checkpoints at all entrances and exits from Eilat. "Our assumption is that it's not one bomber, and there might be more bombers in Eilat right now," Stein said shortly after the attack, adding that in light of the bombing, Eilat police would have to reassess their security assumptions. Following the bombing, police also raised the level of alert nationwide.