Prime Minister Ehud Olmert, Defense Minister Ehud Barak, and Foreign Minister Tzipi Livni met Monday night to decide on the next stages of Operation Cast Lead, which all three agree is aimed at creating a "new security environment" in the South. In a rare consensus among the often feuding triumvirate, Olmert, Barak and Livni all want to continue with the campaign, government officials said. According to a senior government official, the three believe that despite some harsh words from capitals around the world, as well as numerous anti-Israel protests, "there is understanding for what Israel is doing." This understanding was evident, first and foremost, in statements coming out of Washington, which was placing full blame for what was taking place on Hamas, officials said. Olmert, Barak and Livni want to continue to "hit, and hit hard" to create a new security "envelope," the senior official said. The official stressed that the three leaders were making a point of not saying that the objective of the operation was to topple Hamas or destroying it, although the language being used was that of war. Barak, Olmert and Livni were briefed Monday by Chief of General Staff Lt.-Gen. Gabi Ashkenazi, Mossad head Meir Dagan, Shin Bet (Israel Security Agency) head Yuval Diskin and heads of military intelligence. The security cabinet is scheduled to convene Wednesday. Regarding the timeline for the operation, government officials said it was made clear at the outset that this would not be a short, quick-fix operation, but rather a long, complicated action that would take tenacity and perseverance. The official said that there was no sense that the world was about to step in and try to stop the operation. "The feeling is that we have time," he said. Another official said Israel was intentionally keeping the objectives vague, and not spelling out what exactly was meant by creating a "new security environment," so that the government would have maximum flexibility in deciding when and how to stop the fighting. During its presentation to the cabinet, the IDF presented two possible scenarios under which the conflict with Hamas would end. According to the first scenario, a third party, possibly Egypt, Turkey or even a European country, would volunteer to serve as a mediator between Israel and Hamas in an effort to attain a cease-fire between the two sides. Russia, Turkey and Norway have all maintained contact with Hamas, and could conceivably act as mediators, while the rest of the world - which boycotts the organization - would find it difficult to serve as a broker. One diplomatic official said that Israel was not looking for intermediaries to come in and mediate an end to the conflict, and in any case, "no one has jumped in to offer their services." At the moment, there also does not appear to be an effort by Hamas to renew talks over a cease-fire. The Damascus-based Hamas leader Khaled Mashal has, however, contacted several members of the Arab League to discuss the upcoming meeting of a forum at which he is expected to push for a call for a cease-fire. The league is scheduled to convene in Doha later this week. Under the second scenario presented to the cabinet, the current fighting between Hamas and the IDF would create "new understandings" between the two sides, under which Hamas would cease the rocket attacks against the South and Israel would stop its operations. Ultimately, however, the decision of how the conflict ends is up to the political echelon. The framework of a cease-fire with Hamas could be expected to be very similar to the arrangements that were in effect for most of the six months between June and December, under which Israel opened the crossings into the Gaza Strip and in return Hamas stopped its attacks.