Foreign Minister Tzipi Livni is expected to meet her French President Nicolas Sarkozy and Foreign Minister Bernard Kouchner in Paris on Thursday, to discuss diplomatic means to ending the military operation in Gaza. On Wednesday, a senior diplomatic official said that there was no contradiction between Livni's going to Paris to talk about how to end the military action and the security cabinet's decision that the operation would continue. "The operation will continue, but that doesn't mean we are not talking about the day after or the conditions for ending it," the official said. Prime Minister Ehud Olmert said at the end of a five-hour security cabinet discussion that Israel did not launch the comprehensive military operation only to have it end with missiles still falling on the south. "Imagine if after a few days of the offensive we had declared a unilateral cease-fire and a rocket barrage had then hit Ashkelon" Olmert said. "Israel has shown restraint for years; it gave the truce a chance," he continued. "We did this in full knowledge of its price only so that southerners could recover and to give them a period without the worry of a Color Red alert every minute. We told ourselves: 'Let's try it,' but Hamas violated the truce." Olmert said a premature end to the military operation would have severe repercussions for the entire region. Nevertheless, Olmert said, if the conditions of a cease-fire were "right," Israel would consider it. "However, we are not there yet," he declared. Olmert was opposed to a French proposal for a 48-hour "humanitarian cease-fire" that was shot down in a meeting he held late Tuesday night with Livni, Defense Minister Ehud Barak and security chiefs. One official said that Olmert was concerned that a temporary lull in the fighting would play directly into Hamas's hands, because it would give them time to "rearm and regroup." The French idea, which Foreign Ministry officials said never was presented as a formal proposal, never came up at the security cabinet meeting. Olmert received backing for this position from US President George W. Bush, who called Olmert Wednesday from his ranch in Crawford, Texas. Speaking after their phone call, Bush spokesman Gordon Johndroe said the US would like "to see an end to the violence as soon as possible," but that any cease-fire would need to be "sustainable and durable" and not merely allow a brief quiet before Hamas again begins to fire rockets. He refuted suggestions that this posture puts America at odds with United Nations and Quartet statements it has signed onto calling for an immediate cessation of hostilities. "I think President Bush thinks that Hamas needs to stop firing rockets, and that is what will be the first step in a cease-fire," Johndroe told reporters covering the president's stay in Texas. Johndroe said that Hamas also needs to stop smuggling weapons into Gaza - a move that would show it doesn't intend to continue to target Israel. "So I think they're certainly on the same page on that," Johndroe said. Johndroe declined to address the possibility of an Israeli ground operation or the American attitude toward a possible 48-hour cease-fire. He did, however, accuse Syria and Iran of aiding Hamas and abetting the conflict According to a senior Israeli diplomatic official, Israel will keep up the offensive until Hamas agrees not to a 48-hour cease fire, but to a cease-fire that will ensure the security of the South through the establishment of an "apparatus" that will guarantee Hamas will not fire any more rockets at Israel, nor smuggle arms from Sinai. The establishment of this "apparatus" is the focus of the diplomatic activity taking place, including Livni's trip to Paris, the visit of Turkish Prime Minister Recep Tayyip Erdogan to the region for talks in Syria, Jordan, Egypt and Saudi Arabia, and the intense "phone diplomacy" being conducted by US Secretary of State Condoleezza Rice. 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 Monday to push forward a diplomatic solution. Sarkozy may join them, although that has not yet been confirmed. A number of possibilities for a mechanism to guarantee quiet have come up in internal Defense Ministry discussions. The most realistic possibility is said to be for the European Union to enhance the mandate of the EUBAM force that was responsible for running the Rafah Crossing before Hamas's violent takeover of Gaza. The EUBAM force has not been allowed back into Gaza since the crossing was closed in 2007, but defense officials said it was possible that under a new cease-fire the force would return with grater strength and responsibilities. "We would want it to have a stronger mandate that allows the monitors to use force to stop terrorists from entering Gaza or people trying to smuggle weaponry and money," the official said. "At the moment they are just a group of monitors with no real enforcement capabilities." A stronger EUBAM presence could also be augmented by a beefed-up Egyptian force along the Philadelphi Corridor to better combat arms smuggling. The Egyptians have consistently expressed interest in gaining Israeli approval to add to the 750-man force they have on the border. Another idea that has been raised as a guarantee that Hamas would not again fire at Israel when the operation ended is the deployment of a multinational or pan-Arab force in Gaza. This, however, is widely deemed as impractical. "European countries will not want to deploy in Gaza like they did in Lebanon since Hamas will not accept their presence," one official said. "At the same time, a pan-Arab force is also unlikely since Egypt will not want to get involved that deeply in Gaza and there is also concern that some of the force would come from countries hostile to Israel," he said. Although diplomatic officials are talking in terms of a mechanism to guarantee the cease-fire, defense officials said that the more likely scenario was that Israel would have to rely on its own deterrence as the guarantee to prevent Hamas from renewing its rocket attacks. A team has been set up to evaluate Israeli security needs after the operation. It includes OC IDF Planning Division Maj.-Gen. Amir Eshel, head of the Defense Ministry's Diplomatic-Security Bureau Amos Gilad and Olmert's foreign policy adviser Shalom Turgeman. The diplomatic discussions and talks about various mechanisms to ensure the quiet is part of what one official described as a three-pronged Israeli policy. The first prong is to keep up the military pressure on Hamas. The second prong is to expand and upgrade the humanitarian aid into Gaza, and the third prong is discussions with friendly countries to ensure a new "security environment." Regarding the humanitarian aid, government officials said Israel was willing to work and cooperate closely with governments and various humanitarian groups to ensure a constant flow of goods and medicines into Gaza, as well as the evacuation of wounded to Israeli hospitals. One government official said there were two reasons for the emphasis on the humanitarian aid: because it was the moral thing to do, and because it would neutralize international criticism that the military operation was creating a disastrous humanitarian crisis. Bush's spokesman Johndroe spoke positively of Israel's efforts to get humanitarian relief to Gazan civilians, saying that "we're seeing a good flow of humanitarian goods, medical supplies, food into Gaza from various ports of entry." Hilary Leila Krieger and AP contributed to this report.