The release of kidnapped IDF Cpl. Gilad Schalit affair depends on the establishment of a unity government in the Palestinian Authority, Hamas faction head Halil Alhaya said Saturday. According to Israel Radio, the head of Hamas's armed wing, Abu Obaida, corroborated Alhaya's statement, but stressed that even if no agreement on Schalit's release was reached, it would not prevent the PA from setting up a unity government. Abu Obaida added that Hamas wanted an end to the Schalit affair, and said that Egyptian envoys had asked Hamas to move forward on negotiations in the next few days. On Thursday, The Jerusalem Post reported that an agreement had been reached with Hamas over the number of prisoners Israel will release in return for Schalit, and the exchange may take place in the coming weeks. According to defense officials, the prisoner swap will be conducted in three stages. Israel will first release prisoners as a gesture to Palestinian Authority Chairman Mahmoud Abbas. Schalit will then be released into Egyptian custody, and only then will Israel release several hundred additional prisoners, mostly affiliated with Hamas. "The details have been agreed upon and the last issues are being wrapped up," one senior official said. According to the officials, the Egyptian military delegation in the Gaza Strip led by General Burhan Hamed has played a key role in mediating between Israel and Hamas, to the point that they are believed to have been in direct contact with Schalit's abductors. Officials expressed concern, however, that a vacation taken this week by Hamed and his second-in-command would postpone the exchange, which, they said, could take place as early as next week. According to the officials, without Egypt's direct involvement, the deal would never have been reached. "They are responsible for keeping the Schalit issue on the Arab world's agenda," another official said. Yaakov Katz and Herb Keinon contributed to this report.