Israel's expected acceptance of a Cairo-brokered cease-fire with Hamas in the Gaza Strip will "significantly" expedite the release of kidnapped Cpl. Gilad Schalit, a top official involved in the negotiations told The Jerusalem Post on Wednesday. According to the official, while Schalit's release was being negotiated on a second, parallel track to the cease-fire talks, Israel's agreement to a truce in Gaza would "open doors" with Hamas and have an impact on the talks concerning a prisoner swap in exchange for the soldier abducted in June 2006. The Post has also learned that a clause in the Egyptian-brokered cease-fire, which has already been accepted by Hamas, is the reopening of the Rafah crossing between Gaza and Sinai according to the terms of the 2005 agreement reached by US Secretary of State Condoleezza Rice. Hamas, according to the deal, would not be allowed to maintain a presence at the crossing. Based on the 2005 agreement, European monitors would deploy at the crossing and assist Palestinian Authority officers from the Force 17 Presidential Guard - loyal to President Mahmoud Abbas - in running the border terminal. "The acceptance of the terms of the deal will enable the PA to deploy in Rafah and essentially return to Gaza for the first time since Hamas took over last June," the official said. According to top Israeli defense officials, Defense Minister Ehud Barak is leaning toward accepting the cease-fire offer. Egyptian Intelligence Minister Omar Suleiman is expected to visit Israel in the coming days to present the offer to Israel and to hear its response. He will likely meet with Barak as well as with Prime Minister Ehud Olmert. On Wednesday, a dozen small Palestinian factions, including Islamic Jihad and the Popular Resistance Committees, gave their consent to the cease-fire proposal during a meeting with Egyptian officials in Cairo. Last week, Hamas said it would accept a six-month Gaza-first cease-fire, and dropped an earlier demand that the truce also include the West Bank. On Wednesday, diplomatic officials in Jerusalem made it clear that if Egypt and Hamas were waiting for a formal and public Israeli acceptance of the cease-fire agreement, they would be waiting in vain. However, a careful reading of the statement the government put out on the matter shows an Israeli readiness to accept the deal. "We are not in any way referring specifically to what went on in Cairo," Olmert's spokesman Mark Regev said in a carefully worded statement. "We don't need words, but rather tangible steps." Regev said the government's goal was "calm in the South, and for calm to be sustainable it has to embody three vital elements: the total absence of hostile fire from Gaza, the end of terrorist attacks and the complete end of arms transfers into Gaza." This was a marked change in tone for the Prime Minister's Office, which previously had largely dismissed the Egyptian-Hamas talks as little more than an attempt by Hamas to buy time so it could reorganize and re-arm. Regev said that if the three conditions were met in Gaza tomorrow, there would be calm there tomorrow. When asked whether the IDF would stop operations in the West Bank if there were quiet in Gaza, Regev said that if there were quiet in Gaza, Israel would stop operations in Gaza, not in the West Bank. One diplomatic source said that the third condition, ending the arms smuggling into the Gaza Strip, made Egypt a party to the deal and placed a greater responsibility on it to do more to end the smuggling. Even though Suleiman is expected here next week to inform Israel of the arrangements, and even though the Defense Ministry's Amos Gilad has been a frequent visitor in Cairo over the last few months, the Prime Minister's Office continues to say that Israel is not negotiating with Hamas, either directly or indirectly. This is widely viewed as an attempt by Israel to keep other countries from feeling that if Israel were concluding a deal with Hamas through Egyptian mediation, then they too can begin engaging with Hamas. Diplomatic officials said it was no coincidence that this agreement was being finalized on the eve of Rice's visit to the region - she is scheduled to arrive on Saturday night - and a little more than a week before US President George W. Bush visit here. Bush is expected to arrive on May 13, and after taking part in Independence Day ceremonies here and then go on to Saudi Arabia to mark 75 years of US-Saudi ties. From there he is scheduled to go to Egypt. Cairo, according to diplomatic officials in Jerusalem, was certainly eager to broker the cease-fire deal with Hamas before Bush visited, to win US favor. But while Bush will likely praise Egypt for its role, Public Security Minister Avi Dichter on Wednesday criticized Egypt for its handling of the situation in the Gaza Strip. "A problematic terror state has risen that is built on the Hizbullah model," Dichter said during a security cabinet meeting. "There is ongoing weapons smuggling of worrying quantity and quality from Egypt, and this terror state is getting legitimacy from Egypt and maybe even more than that." Since the start of the year, 900 rockets have been fired from Gaza into Israel, the minister told the ministers. Israel was transferring fuel to the Gaza Strip, Deputy Defense Minister Matan Vilna'i reported, but the Palestinians were not picking it up at the Nahal Oz fuel terminal. Olmert, meanwhile, raised the issue of Egypt's attempt to broker a truce with Hamas but said it wasn't appropriate to expand on the issue since Barak was not present. Olmert criticized Barak's absence, saying, "It would have been fitting for him to take part in a ministerial discussion about security issues." Barak missed the meeting because he was at a Golani Brigade training exercise on the Golan. At the end of the drill, Barak told the soldiers: "My gut feeling is to respond immediately and with all our strength to every attack from the Gaza Strip." "However," he continued, "We must act with the proper judgment and at the correct time."