Israel is skeptical that a cease-fire with Hamas will be reached and, therefore, the IDF is preparing for a large-scale military operation in the Gaza Strip, Prime Minister Ehud Olmert has said in recent closed-door meetings while adding that he is letting the process play out in order to show respect for the Egyptian leadership. On Monday, Defense Minister Ehud Barak met with Egyptian President Hosni Mubarak and Intelligence Minister Omar Suleiman in Sharm e-Sheikh and presented them with Israel's proposal for a cease-fire in Gaza - a two-stage deal that would first include a cessation of military operations and terror activity and then a lifting of the siege over Gaza in exchange for the advancement in negotiations over the release of kidnapped soldier Gilad Schalit. Barak told Mubarak that the continued Kassam rocket attacks against Israel would speed up an escalation on the Gaza front and an Israeli military invasion. On Tuesday, Suleiman will meet with a Hamas delegation, led by Moussa Abu Marzuk, deputy head of the group's Damascus-based political bureau, in Cairo and present them with Barak's two-stage proposal. Israeli defense officials said it was likely that Hamas would accept the new terms. During their meeting, Barak also stressed Israel's position that Schalit's release must be part of any cease-fire deal with Hamas in Gaza. A cease-fire, he said, would only be accepted by Israel after a complete cessation of terrorist activity by Hamas and other terror factions, as well as a stop to the smuggling of weapons from the Sinai into Gaza. Kadima MK Shai Hermesh said Monday that Olmert told him in a closed-door meeting last week that while he was "very skeptical" about the chances of reaching an Egyptian-mediated cease-fire, he is letting the process play out in order to show respect to Suleiman. Hermesh lives in Kibbutz Kfar Aza, where resident Jimmy Kedoshim was killed by mortar fire two weeks ago. He said he told Olmert about the suffering of his neighbors and Olmert responded that if Israel's demands were not met in the talks, there would be a military operation in the Gaza Strip that would be "difficult and painful." Olmert's spokesman denied that Olmert would say he was very skeptical of the talks or that they were intended to please Mubarak. But he said Olmert's threat to take action in the Gaza Strip was real and serious. The prime minister told the Kadima faction repeatedly on Monday that "decision time was approaching" regarding whether there should be a major operation in the Gaza Strip. "The perpetual threat has reached a climax," Olmert told the MKs. "Israel cannot allow the current situation in the South to continue." Transportation Minister Shaul Mofaz, Internal Security Minister Avi Dichter and Vice Premier Haim Ramon all urged Olmert in the meeting to expedite an operation in the Gaza Strip. "We know who the address is and who is leading [the attacks on Israeli civilians]," Mofaz said. "I very much hope the time has come to change the policies and change the situation. We don't need to make deals with terrorist organizations." Dichter, who lives in Ashkelon, warned that tragedies would soon outnumber miracles in his city. Ramon acknowledged that Israel is conducting negotiations with Hamas - contrary to the government's own policy on the matter, even if those talks are held via Suleiman. "Negotiations are being conducted with Hamas in contrast to the government's decision, which has determined that it will only be possible to deal with Hamas after it accepts the conditions of the Quartet," Ramon said. "We aren't fighting against a terror organization, but rather a state of terrorism. A terror organization has an area under its control and Israel cannot, in my opinion, make peace with a Hamas state on the southern border." Shani Rosenfelder and Nathan Tobin contributed to this report.