Noam Schalit, father of captive IDF soldier Gilad Schalit, expressed support for the government on Sunday evening and said that he believed there was currently "a one-of-a-kind window of opportunity" to secure his son's release. During a meeting with activists in the Schalit family home in Mitzpe Hila, he praised the government for making the utmost efforts to reach an agreement for Gilad's release. The meeting was convened in light of recent media reports that significant progress had been made in the negotiations between Israel and Hamas. "The Schalit family and the activists believe the current Israeli government is fully determined to fulfill its commitment to bring Gilad back before the next government is formed," Noam Schalit said in a statement. Earlier Sunday, Pensioners Minister Rafi Eitan said that an agreement that will include Schalit's release in exchange for hundreds of Palestinian security prisoners could be signed while Prime Minister Ehud Olmert is still in office. "From my experience, I know that it takes time until a new government is formed, and during that period of about six weeks it is possible to progress on the Schalit matter," Eitan said in an Army Radio interview. He participated in a meeting on Saturday evening with Olmert, Defense Minister Ehud Barak and Foreign Minister Tzipi Livni that focused on the indirect negotiations taking place with Hamas over a new Gaza cease-fire and an exchange for Schalit. The troika also met on Sunday morning, leading to speculation that a long-discussed deal for Schalit was finally at hand. At the same time, Eitan said there had not been any dramatic breakthrough, and that a deal would not be forged in a matter of days. Olmert also took pains to lower expectations, denying at the start of Sunday's regular weekly cabinet meeting that reports of an imminent deal were coming from his office, and urging continued caution when talking about the issue. "I awoke this morning to a stream of media reports regarding Gilad Schalit," he said. "These reports did not come from me or from my office. The continuous activity regarding Gilad's release is coordinated by me. The recent reports are exaggerated and damaging; they are unnecessary. This complex and sensitive process requires due caution regarding all that is said. When there is something to tell the public, I will do so. It is clear that we all hope that the day when Gilad Schalit returns to his family will come as soon as possible. We will not slacken in our efforts to achieve this." Olmert's comments were widely viewed as a slap at Barak, who said in a Channel 1 interview on Friday night that Israel was making great efforts to bring Schalit home. Before the cabinet meeting, Barak said the price for Schalit would be "heavy, and we are not talking about some kind of hocus-pocus" that will bring the soldier back home. Livni said before the meeting that she felt a responsibility to bring Schalit home. "We sent a soldier to defend the State of Israel. The public debate about the price, about what is going on, does not contribute to the cause. The wise person at this time should keep quiet, and that is what I am doing." The Campaign to Free Gilad Schalit released a statement on its behalf and that of the family Sunday night in which it said it believed the government was working hard to fulfill its promise to return Schalit. After almost 1,000 days in captivity the family hopes that his release will now be dealt with quickly to return him healthy and whole to his family. "We understand that we are on the verge of opportunity to return Gilad that has not occurred since he was taken and which might not occur again," the campaign said. Israel had many tools by which to pressure Hamas, such as control of the cash flow and the crossings into Gaza, it said. The crossings should not be opened unless Gilad is freed, the campaign said. The family and the campaign have been strengthened by the promises made by cabinet members that they are doing everything they can at this time, the campaign said. It added that based on information in the press it was cautiously hopeful. It thanked the public for its support as well as the residents of the South and the soldiers who risked their lives to fight in Gaza. Among the terrorists Hamas is reportedly demanding in return for Schalit are those behind some of the worst terrorist atrocities of the second intifada, including the Pessah eve massacre at Netanya's Park Hotel in 2002, in which 30 people were killed and 140 were wounded. The London-based Al Hayat on Sunday quoted Palestinian sources as saying Israel had agreed to release 1,000 Hamas prisoners in exchange for Schalit - including Fatah-Tanzim militia head Marwan Barghouti - during the second phase of a Gaza cease-fire. Barghouti is currently serving five life sentences for five murders and 40 years imprisonment for attempted murder. According to the report, which was not confirmed in Jerusalem, the first phase of the cease-fire would include the cessation of all hostilities between Israel and Hamas and a Hamas commitment to refrain from firing rockets into southern Israel for 18 months. An Egyptian official told The Jerusalem Post on Sunday: "We are optimistic that a new tahadiyeh [cease-fire] will be reached within days." However, Muhammad Nazzal, a Hamas leader in Damascus, said there was "nothing new" to report in the Schalit case. Nazzal said Hamas was waiting for a "positive development" from the Israelis. He also said the Islamist group would not rush to an agreement just because of the Israeli election. "We do not set our agenda according to others' calendars or schedules, meaning that we are not concerned about the Israeli elections... We are concerned about signing a decent deal," he told Al-Jazeera. Tovah Lazaroff and Brenda Gazzar contributed to this report.