Prime Minister Ehud Olmert will tell Egyptian President Hosni Mubarak at a meeting scheduled for Tuesday that a Hamas breach of the Gaza Strip cease-fire will be met by a harsh Israeli reaction, officials in Olmert's office said Thursday evening - expressing continued concern that the truce that went into effect in the morning, and held throughout the day, might be short-lived. "The Egyptians need to understand that if the lines are crossed, we will have to act," the officials said. Government sources stressed that maintaining good relations with the Egyptians, who had worked hard to broker the cease-fire, was one of the the factors that went into the government's decision to accept it, rather than initiate a major military operation. As such, the sources said, Olmert wanted to go to Egypt and "reap the benefits." He is expected to impress upon Mubarak the importance of ending the captivity of Gilad Schalit, and urge him to use his leverage with Hamas to get them to show flexibility on the list of prisoners they are demanding for Schalit's release. According to Egyptian sources, Egyptian Intelligence chief Omar Suleiman, on one of his recent visits to Israel, said that once the cease-fire took effect, intense negotiations for the release of Schalit would resume immediately. The sources said that Ofer Dekel, the prime minister's point man on the prisoner issue, is expected in Cairo early next week to begin intensive negotiations through Egyptian mediators. Israeli sources also said that according to the cease-fire agreement, the Rafah crossing from the Gaza Strip into Egypt will not be opened until there is significant progress on the Schalit issue, perhaps not until Schalit is transferred to Egypt as part of a multi-staged release arrangement. Israel, in the meantime, is bracing for growing calls around the world to establish contact with Hamas, expected as a result of the cease-fire deal. The concern is that voices will be raised saying that since Israel struck a deal with Hamas, there was no reason why other countries should not be able to talk to the organization. Foreign Minister Aryeh Mekel said that Israel's position on the matter is that the cease-fire was initiated and brokered by the Egyptians. "There is not in the cease-fire anything to give any legitimacy to Hamas, and Israel will continue to lead the policy to continue isolating Hamas in the international community," he said. Mekel said that the international community's response to the cease-fire was overwhelmingly positive. For example, Quartet envoy Tony Blair issued a statement calling the period of calm a "positive development," and saying that Hamas now had to "demonstrate their true intentions to the people of Gaza, Israel and the world." "If they want peace and prosperity, it is on offer," Blair said, referring to the negotiations between Israel and the Palestinian Authority. Defense Minister Ehud Barak said Thursday that he did not know how long the cease-fire in Gaza would last but that it was worth trying regardless. "We look with open eyes at the situation and understand it's fragile, but we prefer to give it a chance," he told reporters in Paris, where he was meeting with his French counterpart Herve Morin and attending the annual Paris defense expo. Asked if he was optimistic, Barak replied: "A pessimist is an optimist with experience." In an interview with France's Le Monde newspaper, published Thursday, Barak was quoted as saying, "This cease-fire, we don't know how long it can hold, two days or two months." "Historically we have been on a collision course with Hamas. But it nevertheless makes sense to seize this chance," he was quoted as saying. "If (the cease-fire) breaks, we will have a stronger legitimacy. If it holds, it is an opportunity." Other officials were vague in their predictions regarding the cease-fire, with some claiming it will last a week and others saying it had the potential to last several months. All the officials agreed that the coming weeks were considered the "crucial period" during which both sides will be anticipating the other breaking the quiet. "We are ready for all developments and can be inside Gaza in a massive operation right after a breakdown," a top IDF officer said Thursday. "At the moment we are doing everything we can to ensure that the cease-fire lasts." Deputy Defense Minister Matan Vilna'i held a security assessment at his office on Thursday to discuss the current situation at the crossings into the Gaza Strip. Defense officials said that based on the format of the cease-fire, Israel will increase the amount of food and clothing it allows into Gaza by 30 percent on Sunday, assuming that the truce is held by Hamas. A week later and following additional daily assessments, Vilna'i said he would begin approving the transfer of cement, gravel, metal and fuel. Over the past year, Israel has limited the transfer of raw materials into Gaza out of fear that they were being used in the production of Kassam rockets. Vilna'i instructed the Crossings Directorate in the Defense Ministry to begin work on fixing the Kerem Shalom Crossing, which was severely damaged several months ago when a Palestinian truck bomb exploded inside. The damages are estimated at several million shekels but officials said that Sufa - currently the only operational crossing - could only facilitate 100 trucks a day. The number will begin to increase next week. The cease-fire began Thursday morning at 6 but was preceded by an Israeli attack in the Gaza Strip. A Hamas operative was killed and two others were wounded in an IAF strike in central Gaza, at about 4 a.m. Thursday, just two hours before the Gaza truce began. Palestinians also claimed that the Israeli Navy had fired four shells into waters off the Gaza coast minutes after the cease-fire went into effect. The IDF confirmed it had fired warning shots into the air after Palestinian fishermen entered Israeli territorial waters. AP contributed to this report.