Israel Police decided to increase its presence in main cities and crowded places, fearing that more attacks will follow Monday's suicide bombing in Dimona. According to Israel Radio, the alert level was raised to "C" which is one level below the highest level of emergency. Police said many more police officers will be patrolling the southern, Jerusalem and Tel Aviv districts. Security officials also said Tuesday that the amount of intelligence alerts have increased considerably since the attack. In a statement issued early Tuesday by the office of spokeswoman Dana Perino, the White House said it strongly condemned the bombing. "We extend condolences to the family of the innocent victim killed in this brutal attack and wish those wounded a rapid recovery," the White House said. "We also condemn those terrorist groups, including Hamas, which condone these horrific actions. We call upon the leaders of the Palestinian Authority, who condemned this attack, to redouble their efforts to act against terrorism." On Monday, Reuters reported that Hamas's armed wing, Izaddin Kassam, claimed responsibility for Monday's suicide attack which killed a woman and wounded some 40 other people, saying that he bombers came from Hebron and not the Gaza Strip. However, Hamas's representative in Lebanon, Osama Hamdan, denied the report, saying the group was not linked to the bombing. The IDF raided Hebron late Monday night but defense officials said it was premature to determine the terrorists' origin. Also Monday night, the IDF was conducting searches not far from Kerem Shalom along the Israeli-Egyptian border. IDF sources said soldiers had discovered tracks showing that someone, possibly a terrorist, had crossed the border into Israel. The attack initially fueled IDF fears that the terrorists had infiltrated Israel from Sinai after entering Egypt following the collapse of the border wall between Sinai and the Gaza Strip two weeks ago. Defense officials said additional terrorists were believed to have infiltrated Sinai over the past week and were making efforts to enter Israel via the fenceless border with Egypt. The IDF was maintaining a high level of alert along the border with Egypt and Highway 10, which runs along the border, remained closed to civilian traffic. Defense officials told The Jerusalem Post, however, there was a growing opinion the terrorist duo had indeed come from the West Bank and had infiltrated the Negev via the 26-km. gap in the southern section of the West Bank security barrier. Israel pledged to hit back at the terrorist organizations that dispatched two suicide bombers on Monday to Dimona, where one blew himself up. In what appeared to be a response to the attack, the IDF and the Shin Bet (Israel Security Agency) killed a top operative of the Popular Resistance Committees who officials said was responsible for countless Kassam rocket attacks against the western Negev. It was not clear if the terrorist was involved in the Dimona bombing. On Monday night, authorities announced the the woman killed in the attack was 73-year-old Lyobov Razdolskya, a Dimona resident from the former Soviet Union. Her husband was still in the hospital in critical condition. She was scheduled to be laid to rest at the new cemetery in Beersheba at 16:00 p.m. Tuesday. All of the casualties were taken to Beersheba's Soroka University Medical Center, almost 30 minutes away; hospital spokeswoman Inbal Guter said that after hours of surgery, the most seriously wounded victim's condition had been upgraded to "very serious." As civilians and emergency crews rushed to the scene of the bombing in Dimona's old commercial center, civilian responders discovered that the second terrorist, who police believe had planned to detonate his explosives once a crowd gathered, was still alive and trying to detonate his bomb belt. Two policemen arriving on the scene, Magen unit commander Ch.-Supt. Kobi Mor and bomb squad member Special Master Sergeant Gilad Bastiker, ran toward the terrorist. Taking cover, a quick-thinking Mor shot the terrorist in the head from about 10 meters away. "They were concerned that if they shot anywhere else, it could detonate his explosive belt," said Southern District Police chief Cmdr. Uri Bar-Lev. Also Monday, Egyptian security forces claimed to have apprehended a Gazan, armed with a bomb, after he had infiltrated Egypt's side of Rafah. Referring to the possibility that the Dimona attackers crossed into Israel from Sinai, officials said that Defense Minister Ehud Barak had decided to speed up the planning of a fence along the Egyptian border. Defense officials were in touch with Cairo throughout the day and said they urged Egyptian security officials to increase security along their side of the border. A number of terrorist groups claimed responsibility for Monday's attack in Dimona. Fatah's Aksa Martyrs Brigades claimed responsibility for planning the attack, saying it had been in the works for about a month. In a press conference convened by the group, the two bombers were named as Musa Arafat, from Khan Yunis in the Gaza Strip, a member of the Abu Ali Mustafa Brigades - the armed wing of the Popular Front for the Liberation of Palestine, and Aksa operative Luai Al Aghwani from Gaza. Prime Minister Ehud Olmert said the attack was a "painful reminder" that Israel must remain vigilant and be prepared for attacks throughout the country. "We are waging a war on terror," he said during a meeting of the Kadima faction. "It is continuing without bounds and we will get to everyone involved in terror activity." The last suicide bombing in Israel occurred in January, 2007, when a Palestinian bomber blew himself up in an Eilat bakery, killing three Israelis. The bomber, who came from Gaza, infiltrated Israel via the Egyptian border. Eyewitnesses to Monday morning's attack said Dimona's old commercial center was fairly busy when the two terrorists arrived with bombs strapped to their bodies. At least one of them was wearing a thick ski jacket. Passing a lottery stand, the first terrorist detonated himself in front of a store selling jewelry, socks and winter accessories. It was the first terrorist attack in the history of Dimona, a Negev town better known for unemployment than for security issues. Dozens of residents gathered in the downtown area, watching ZAKA rescue and recovery teams and police sappers at work. It took more than three hours for sappers to neutralize the second terrorist's explosive device, as experts tried to identify its components and source.