The chances of a massive IDF ground incursion into the Gaza Strip seemed to fade Thursday, as Jerusalem began to brace for an international full-court press expected to begin Monday to bring the fighting to an end. With Foreign Minister Tzipi Livni in Paris on Thursday discussing diplomatic solutions with French President Nicolas Sarkozy and Foreign Minister Bernard Kouchner, Prime Minister Ehud Olmert was speaking by phone with world leaders as various suggestions for ways to ensure that Hamas would not return to firing on Israel or to smuggling arms were on the table. Security sources told The Jerusalem Post that they doubted a major ground offensive would now be ordered, and that a cease-fire would likely be concluded within a week. The security sources said they believed Hamas would be pressured by the Arab states and Turkey to honor an eventual cease fire. These sources added that Israel would need to work with Egypt to prevent a resumption of arms smuggling that would strengthen Hamas. Senior government sources said Egypt, which they praised for playing a very constructive role throughout the crisis, would "have an important role to play when the quiet is established." The sources said that the way the Egyptians have managed their border with Gaza throughout the crisis, keeping the Palestinians from breaching the Sinai frontier as happened in the past, indicated that Cairo - because of its own interests - would likely play a much more effective role in the future to keep Hamas from rearming once the current IDF operation came to an end. While Israeli leaders have not formally spelled out what the conditions are for ending the operation, government sources have said that one such condition is a mechanism to ensure that Hamas will stop firing at Israel and no longer smuggle arms. Egypt, the sources said, was expected to play a large role in whatever new framework is developed. Livni, in a an interview Thursday night on Channel 2 after meeting with Sarkozy, pointedly refused to discuss at what the point Israel would suspend its military operations, saying that is just what the Hamas leaders wanted to know, "when it would all pass and they could come up from their bunkers for a breather." Sarkozy is now scheduled to meet in Jerusalem with Olmert on Monday evening, as part of a regional visit that is expected to underline efforts to bring about a diplomatic end to Operation Cast Lead. In addition, the foreign ministers of France, the Czech Republic and Sweden, along with Benita Ferrero-Waldner, the European Commissioner for External Relations, are all expected to arrive the same day as well, something that will give the diplomatic efforts a higher profile and greater sense of urgency. Livni said the French idea for a 48-hour humanitarian cease-fire has been removed from the agenda, and that she explained in Paris that "there is not a humanitarian problem in Gaza, the crossings are open." According to Livni, the operation has already succeeded in changing Hamas's equation that it can fire with impunity on Israel, and that Israel would "restrain itself, won't respond, or will respond in a measured way." Egypt's Foreign Minister Ahmed Aboul Gheit, meanwhile, said Hamas must ensure rocket fire stops in any truce deal, criticizing the organization again for giving Israel a "golden opportunity" to launch its military operation. Aboul Gheit's comments Thursday come as Turkey's Prime Minister Recep Tayyip Erdogan met with Egypt's President Hosni Mubarak, part of a tour to develop an Egyptian-Turkish initiative to end the violence. The initiative calls for a halt to Israel's offensive, a return to a truce and an international mechanism to ensure the opening of Gaza's border crossings. Israeli officials said the Turkish role was to "market the Egyptian idea to the Arab world, first and foremost to Hamas and Syria who, because of Egypt's words and actions during the crisis, don't see it as a "fair broker." In addition to pushing the Egyptian idea, the assessments in Jerusalem are that the Turks are also looking for ways to bring about a Hamas-Fatah rapprochement that would allow the PA to regain control of Gaza. Livni said after meeting Kouchner that "this war with the extremists is necessary in order to move the diplomatic process forward toward a two-state solution." One senior diplomatic official said afterward that only a weakened Hamas, that could not scuttle all diplomatic moves with rocket attacks from Gaza, would enable Israel and the Palestinian Authority to move forward in the diplomatic process. Meanwhile, the Security Council held an emergency meeting on New Year's Eve on an Arab request for a legally binding and enforceable UN resolution that would condemn Israel and halt its attacks in Gaza. But the draft resolution circulated by Libya on behalf of the 22-member Arab League Wednesday night was immediately rejected by the United States as "unbalanced" and "one-sided" because it makes no mention of halting the Hamas rocketing of southern Israel that led to the Israeli offensive. Riyad Mansour, the Palestinian UN observer, said Arab nations would be working "day and night" to get council approval of a binding resolution "that would condemn the crimes committed by Israel and stop the military aggression, and provide protection for the Palestinians and lift the siege." At the start of Wednesday night's council meeting, UN Secretary-General Ban Ki-moon again condemned "the indiscriminate rocket attacks by Hamas terrorists and the disproportionality of the continuing Israeli military operation." He said he was "profoundly troubled" that the council's call for an end to the violence had gone unheeded and demanded that the parties "step back from the brink" and observe an immediate cease-fire. While welcoming efforts to end the conflict, including by Arab and European leaders, Ban reiterated that "not enough has been done and more is urgently required." He called on all members of the international community, especially those in the region, "to exert what influence they have on the parties to end this violence now." AP contributed to this report.