The release of captive soldier Gilad Schalit is expected to be high on the agenda of talks when Prime Minister Ehud Olmert meets Egyptian President Hosni Mubarak Tuesday morning in Sharm e-Sheikh. Olmert is expected to urge Mubarak to both press Hamas, which has held Schalit since June 2006, into being more flexible on the names of the prisoners it is demanding in return for Schalit, and also to keep the Rafah crossing closed until significant progress is made on the Schalit track. In addition the two leaders are expected to discuss the indirect talks taking place with Syria, the negotiations with the PA and the Gaza Strip cease-fire. Speaking at a Kadima meeting on Monday night, Olmert said he had always promised that quiet would be restored "one way or another" to residents of the south who live along the Gaza border. "I am among the first to understand the pain of the southern residents and to identify with them," he added. "Just like we stopped the terror in [the West Bank] almost completely, we will stop it in the South. At this point, it has been halted mainly because they [Hamas] understand the price they will pay if it continues," Olmert said. A diplomatic source said Olmert's trip to see Mubarak so soon after the cease-fire agreement, reached only last week, was an attempt to capitalize on the positive impact Israel's acceptance of the cease-fire could have on Israeli-Egyptian ties. Egypt was actively involved in brokering the cease-fire, devoting much time and effort to the matter, and concern of what an Israeli rejection of the plan could do to Israeli-Egyptian efforts was one element, diplomatic sources have confirmed, behind Israel's acceptance of the cease-fire deal. Egyptian sources said that one element of the deal was agreement that once it was accepted, intensive negotiations through an Egyptian mediator would take place in Cairo for the release of Schalit. According to the sources, Israeli and Hamas teams would be in the "same place," though not in the same room, and Egyptian mediators would shuttle between them to conclude the Schalit deal. Olmert's point man on the prisoner issue, Ofer Dekel, is expected to go to Cairo on Tuesday as well. On Monday evening, Noam Schalit met with French President Nicolas Sarkozy, who is on a three day trip to Israel. Schalit had met with Sarkozy once before in France just as the election. Since both he and his son, Gilad, hold dual Israeli-French citizenship, Noam asked Sarkozy in both meetings to help free the young man. Sarkozy "promised to do as much as he could," Schalit told The Jerusalem Post. But while his reception from Sarkozy was warm, Schalit was surprised to hear that former former IDF chief of general staff Maj. -Gen. (res.) Moshe Ya'alon had warned against paying too high a price to release captive soldiers. "I was startled because he was chief of staff and [was raised] on on the IDF principles," said Noam. "No one, not Boogi or anyone else, has the right to say that unless you are talking about your own son," Noam said. On Tuesday evening Noam and his wife Aviva, as well as their family and supporters, plan to hold a rally opposite the prime minister's residence in Jerusalem. On Wednesday, they have organized an event in their home town of Mitzpeh Hila in the upper Galilee to mark two years since Gilad's kidnapping. Tovah Lazaroff and Gil Hoffman contributed to this report.