Giving a conditional green light for a deal with Hamas to free captured soldier Gilad Schalit, Israel on Tuesday reportedly gave a German mediator a list of 125 Palestinian key security prisoners and the terms under which it would agree to their release. In many cases, Channel 1 reported, their release would be contingent on their deportation. The 125 names were selected by Israel from a list of about 300 names originally presented by Hamas last spring, and subsequently reduced to some 180. According to Channel 1, Israel was firmly opposed to the release of any Israeli Arabs on the original Hamas lists, and to the release of some of the gravest offenders with "blood on their hands." The German diplomat was to meet with Hamas representatives in Gaza later on Tuesday night or on Wednesday morning and present the terrorist group with the Israeli conditions. The Hamas leadership in Damascus is reportedly opposed to a deal that would include the deportation of a significant number of released prisoners. According to the Prime Minister's Office, the inner cabinet has given Israeli mediator Hagai Hadas a green light to continue negotiations with Hamas to secure Schalit's release. The inner cabinet is reportedly looking to go forward with the deal as long as Israel doesn't release certain prisoners with "blood on their hands" back into the West Bank or inside the Green Line. The inner cabinet, known as the forum of seven, is made up of Prime Minister Binyamin Netanyahu (Likud), Defense Minister Ehud Barak (Labor), Foreign Minister Avigdor Lieberman (Israel Beiteinu), Interior Minister Eli Yishai (Shas), Intelligence Agencies Minister Dan Meridor (Likud), Strategic Affairs Minister Moshe Ya'alon (Likud) and Minister-without-Portfolio Bennie Begin (Likud). The forum met late into the night on Monday in what was described by insiders as a final marathon discussion on the prisoner-swap agreement that would end Schalit's three-and-a-half-year Gaza captivity. A government official said the question of whether certain prisoners would return to the West Bank or be deported was "clearly" an issue. He spoke on condition of anonymity because he was not authorized to release details of the talks. Former Fatah-Tanzim leader Marwan Barghouti, who is serving five life sentences for five murders, would be allowed to return to his West Bank home, a Palestinian close to the negotiations said. Hamas has also agreed that several other hard-core prisoners be deported, he said. However, the Damascus-based leadership of Hamas opposes the deal and will pressure the organization's Gaza leadership not to accept it, Channel 1 also reported. Meanwhile, Fox News reported that Netanyahu is hoping the deal with Hamas will fail and the Islamist group will be blamed. The Prime Minister's Office denied the report, however. Also on Tuesday, the prime minister met with representatives of the Almagor Terror Victims Association, who reportedly expressed opposition to the proposed deal, which would include the release of hundreds of Palestinian prisoners, including many who have murdered Israelis. Almagor has suggested alternative means of pressuring Hamas to release Schalit, including increased sanctions and stricter conditions for Hamas prisoners held in Israel. Barak said on Tuesday that Israel had a responsibility to bring the captive tank gunner home, but not if the cost is too high. "This is a sensitive time and it would be wrong to expound upon the topic, but we, as those who sent Gilad, feel a responsibilityâ€¦ to make every feasible and worthy move to bring Gilad home, though not at any price," he said, during a visit to high school students in Rishon Lezion. After more than four hours of talks by the forum of seven, the Prime Minister's Office released a statement early on Tuesday morning saying only that instructions were given to the negotiating team about "the continuation of efforts to bring Gilad Schalit home safe and sound." Dr. Sufiyan Abu Zaydeh, a senior Fatah official and former Palestinian Authority minister for prisoner affairs, called on Israel to okay the deal to release Schalit as soon as possible. Abu Zaydeh was invited to the Knesset on Tuesday to address a forum on the two-state solution, and in the course of his remarks, was asked by event organizers in Kadima to comment on the Schalit negotiations. "One name more, one name less. One more prisoner, one less prisoner. Forget about all that, and do the important thing quickly," said Abu Zaydeh - himself a former Israeli prisoner. He added that the proposed deal - said to involve around 1,000 prisoners, was far from releasing all of the approximately 10,000 Palestinians held in Israeli prisons. "As long as there are prisoners and as long as the conflict continues, there will be people who seek solutions outside of the framework of negotiations," he said. Rebecca Anna Stoil contributed to this report.