Egypt has offered to mediate a cease-fire with Hamas if Israel halts all military operations in the Gaza Strip, The Jerusalem Post has learned. The Egyptians have told Jerusalem they are prepared to renew the dialogue with Hamas that Cairo believes can lead to a long-term cease-fire as well as reconciliation between Hamas and Fatah. Meanwhile, Egyptian President Hosni Mubarak further angered Hamas on Tuesday by insisting that he would not open the Rafah crossing between Sinai and Gaza unless it was controlled by the Palestinian Authority, and European monitors required under a 2005 agreement were present. Otherwise, opening it would "deepen the breach" between Hamas and PA President Mahmoud Abbas, whom Egypt considers the legitimate leader of the Palestinians, Mubarak said. Israeli officials said that despite current tension between Hamas and Cairo over Egypt's refusal to open the Rafah crossing, Hamas would have no option but to rely on Egypt to broker a cease-fire. Both Turkey and Qatar have taken some steps toward trying to mediate as well, but neither has the same standing in the region as Egypt. It is not clear that Israel would rely on Qatar, a country with which it does not have full diplomatic relations, and Turkey, one Israeli official said, just didn't have as good an understanding of the situation on the ground or the players involved as did Egypt. "At the end of the day, Hamas will not have a choice but to rely on Egypt," the officials said. According to the officials, Israel has kept open a channel of communications with Egypt throughout the current Gaza crisis, and was in constant contact with Cairo about the developments on the ground. The officials said the Egyptians were interested in an immediate cease-fire, perhaps for 48 hours, followed by a return to the previous "security calm." They also want to negotiate the opening of the border crossings into Gaza, particularly Rafah, under international supervision, perhaps more stringent than when the EU forces monitored the crossing from the end of 2005 until Hamas's takeover of Gaza in the summer of 2007. Israeli officials expressed optimism that once Operation Cast Lead ended, the Egyptians would step up efforts to stop the smuggling from Sinai into the Gaza Strip, particularly since it was now apparent what Hamas had brought in. Egypt, for its part, believes that following the IDF operation Israel might be open to letting Egypt increase the number of border policemen it has deployed along the Philadelphi Corridor between Sinai and the Strip. Following Israel's withdrawal from Gaza in 2005, Egypt was permitted to deploy 750 policemen along the border with Gaza, to be used to locate and destroy Hamas weapons-smuggling tunnels, in an exception to the limits placed on Cairo by the Egyptian-Israeli peace treaty. Since then, Egypt has persistently asked Israel to allow an increase in the size of the force, but the defense establishment has been opposed. The sense in Cairo is that Israel may change its mind following the operation in Gaza, and also because of a recent dramatic improvement in Egypt's efforts to locate and destroy tunnels with the force it currently has deployed there. Egypt has made no secret of its anger toward Hamas and has relayed messages to Jerusalem that it is in favor of Israel's efforts to stop the rocket attacks against the South. Egypt has, however, called on Israel to stop the operations in Gaza, which it says are disproportionate. The Egyptians believe that Hamas has sustained a severe blow to its regime as a result of the air strikes and was likely to now accept a new truce. Meanwhile, Cairo has launched a public relations campaign to defend its response to Israel's offensive against a growing chorus of critics. Mubarak defended his country's handling of the Rafah border crossing. Warning of an Israeli intention to divide the West Bank from the Gaza Strip, Mubarak said: "Egypt will not contribute to the perpetuation of this division [between Hamas and the PA] by opening the Rafah crossing in the absence of the Authority and European Union monitors [and] in violation of the 2005 agreement." The Rafah border is regulated by an agreement Egypt signed with the PA and the EU after Israel left the Strip in 2005. Despite the pact, Egypt has opened the Rafah border for humanitarian cases, and is "exerting continuous efforts" to get Israel to open its crossings with the Gaza Strip, Mubarak said during a press conference in Cairo. On Tuesday, he accused critics of seeking "political gain" from Palestinian suffering, saying "Palestinian blood is not cheap." While the right to resist occupation was "a fixed and legitimate right," he said, "the resistance [Hamas] is responsible for its people." The IAF operation in the Gaza Strip has unleashed an onslaught of anger across the Middle East, directed as much at Egypt as against Israel. Protesters have attacked Egyptian embassies, and Hamas leaders accuse Cairo of helping Israel's blockade and even giving a green light for the offensive. The anger is a sign of the gulf between an Arab public outraged by the killings of Palestinians, and their US-allied governments, which oppose Hamas's domination of the Gaza Strip and view the terrorist group as fueling trouble in the region. Demonstrators broke into the Egyptian Consulate in the Yemeni city of Aden on Tuesday, trashing the interior, throwing computers out the window and burning the Egyptian flag on the roof. In recent days, Lebanese police have fired tear gas to keep protesters away from Egypt's embassy in Beirut, and demonstrators in the Lebanese city of Sidon chanted slogans denouncing Mubarak as "a pig" and a "collaborator" with Israel. Mubarak said Tuesday that he gave orders to the open the border to allow injured Gazans to leave the Strip and be transferred to Egyptian hospitals, as he has done for other humanitarian cases. Meanwhile, Arab foreign ministers are set to meet on Wednesday to forge a united position and to decide whether an emergency Arab summit is needed to help resolve the conflict. But as of Tuesday, the states were still divided on how best to tackle the IDF offensive. Qatar and other states have called for an emergency summit of Arab leaders. Qatar has offered to host such a summit as early as Friday. But Egypt's Foreign Minister Ahmed Aboul Gheit said this week that an Arab summit "could be dangerous and subject to criticism, especially if it does not result in practical measures." AP contributed to this report.