An elderly woman was killed by a Kassam rocket that scored a direct hit on a western Negev community Monday evening, hours after Israeli leaders said they were leaning toward accepting an Egyptian cease-fire deal with Hamas. Shlomit Katz, 75 of Kibbutz Gvar'am, was killed while visiting Moshav Yesha in the Eshkol Regional Council. The deadly attack came four days after a mortar shell barrage killed Jimmy Kedoshim, 48, a father of four, as he stood in the yard of his house in Kibbutz Kfar Aza in the Negev. Islamic Jihad claimed responsibility for Monday's attack, after which certain defense officials warned against accepting the Egyptian-proposed cease-fire with Hamas and called for a military response to the continued rocket fire. A half-dozen rockets fell in the western Negev area Monday, including one that landed in Ashkelon. Despite the escalation in violence, officials close to Defense Minister Ehud Barak said that Israel was leaning toward accepting Egyptian Intelligence chief Omar Suleiman's truce offer, which was presented to the defense minister during a breakfast meeting at Barak's Tel Aviv home earlier in the day. Israel plans to first gradually accept the offer and later turn it into a full-fledged cease-fire following Gilad Schalit's release. Defense officials said that if the Egyptian-brokered cease-fire did not last, Israel would most likely embark on a large-scale operation in the Gaza Strip against Hamas. "If the cease-fire doesn't work, our alternative to stopping Hamas's attacks is by invading Gaza," a senior official said. During their meetings with Suleiman, both Barak and Prime Minister Ehud Olmert stressed the cease-fire needed to include the release of Schalit as well as an end to all forms of attacks on Israel from the Gaza Strip and a cessation of Hamas's arms build-up there. Suleiman told Barak that the acceptance of the deal would not bring Schalit's immediate release, but would expedite the process. Barak also stressed that Israel would not continue to restrain itself from responding to the continuous missile fire from the Gaza Strip, and that Israel would be forced to take more stringent military steps if the attacks did not stop. The defense minister also told Suleiman that Israel would demand assurances from Egypt that it would increase its efforts to curb weapons smuggling under the Philadelphi Corridor. Suleiman said that Egypt was making more efforts and hoped to receive US-made tunnel-detection systems in the coming weeks to add to those efforts. Suleiman, according to officials in the Prime Minister's Office, said he would take those conditions back, discuss them with Hamas, and return with an answer. No time frame, however, was given. The officials said that Suleiman, who has been trying to broker a cease-fire in the Gaza Strip for weeks, did not come with any new proposal. Olmert and Suleiman met for some 90 minutes in discussions that Olmert's office characterized as "good." The first stage of the deal calls for a cessation of IDF action, Hamas terror activity as well as the opening of the Israeli crossings into Gaza. At a later stage, the Rafah crossing is slated to be opened. Sources in Olmert's office said that three weeks ago Olmert and Egyptian President Hosni Mubarak scheduled a meeting in Sharm e-Sheikh sometime after the World Economic Forum meeting there this weekend. It is widely expected that when the two do meet, it would be to finalize the agreement. So far no date has been set. Olmert's spokesman Mark Regev, meanwhile, denied that Suleiman's shuttle between meetings with Israeli officials and that Hamas officials represented an indirect form of negotiations. "There are no negotiations, with Hamas," Regev insisted. "Israel and Egypt have a common interest in trying to maintain stability in the south. Israel cannot continue to tolerate the daily barrage of rockets, so either the attacks will cease or Israel will have to stop them. We don't have a great desire to escalate in the south, and if it is possible to achieve clam, that is obviously our preference, and the Egyptian's preference." Government sources, meanwhile, said that Israel's insistence that Schalit be included in the deal - knowing Hamas would not agree - was a way to gracefully get out of an agreement that Israel is not enamored with. According to these sources, Israel is concerned that Hamas would use the cease fire to strengthen itself in Gaza, something Israel wants to prevent. According to the sources, conditioning the agreement on the release of Schalit is something the public would back. Foreign Minister Tzipi Livni, meanwhile, also told Suleiman that there would be no arrangements in Gaza as long as Schalit remained in captivity. She also stressed that there could not be quiet calm in the Gaza Strip until the arms smuggling and the Hamas weapons build-up ceased. Suleiman also met Industry, Trade and Labor Minister Eli Yishai, from Shas, who has said he would be willing to meet with Hamas to secure Schalit's release.