Four years ago, Egypt was ruled by pro-Western Hosni Mubarak, who helped keep Hamas isolated. This time around, Hamas had an effective ally in Mubarak's successor, Mohammed Morsi, like the Gaza Islamists a member of the region-wide Muslim Brotherhood. Morsi quickly emerged as an effective mediator, since he already had the trust of Hamas and Israel did not want to risk hurting its ties with the Arab world's most populous nation.
Israel's deputy prime minister, Dan Meridor, underscored Egypt's importance to Israel, suggesting they share security concerns, including making sure that "Gaza does not become a source of eruption endangering the stability of the region."
Egypt's sway over Hamas meant that the Islamists scaled back their demand to negotiate a detailed border deal with Israel before halting fire. In the end, Hamas agreed that a 24-hour period of calm would lead to negotiations on the new arrangements.
On Thursday evening, a senior Israeli official arrived in Cairo for follow-up talks with Egyptian intelligence. Earlier in the day, the Egyptian intelligence chief had met with the top Hamas leader in exile, Khaled Mashaal, and the head of the smaller sister group Islamic Jihad, Ramadan Shalah, according to Shalah's deputy Ziad Nakhaleh.
The apparent formula on the table is that Hamas halts weapons smuggling into Gaza in exchange for an easing of the Gaza border restrictions imposed by Israel and Mubarak after the Hamas takeover of Gaza more than five years ago. Morsi has eased restrictions on the main Egyptian crossing but not completely thrown it open as Hamas would like.
Hamas demands complete freedom of movement in and out of Gaza, while balking at the idea of demilitarizing the territory. However, an Israeli security official, speaking on condition of anonymity because he was not authorized to discuss internal deliberations with reporters, said Israel would link the two.
Israel's military, which also deals with Gaza's border crossings, has presented possible plans for easing restrictions to Israel's political leaders, the official said.
This includes allowing badly needed building materials for reconstruction into Gaza for the first time since 2007 and permitting trade between Gaza and the West Bank, the two territories that flank Israel and that Palestinians hope will one day make up the bulk of their state. Eventually, Gaza-West Bank travel could also be considered, he said.
Such border changes, if approved by Israel's political leadership, could help reboot Gaza's battered economy, shore up Hamas' popularity and extend the Islamists' rule. In exchange, Hamas would have to stop arming itself and essentially give up what is now a main pillar of its power.
Hamas' main gains have been in the political arena. Foreign ministers from the region rushed to Gaza over the past week to show support for Hamas, while the U.S. and Israel grudgingly acknowledged Hamas' central role by conducting indirect talks.
Hamas also managed to show up Abbas, its main Western-backed political rival who -- rendered largely irrelevant -- watched events unfold from the sidelines.
Netanyahu's willingness to negotiate a truce deal with Hamas, while refusing to engage Abbas on the same terms as previous Israeli prime ministers, reinforced many Palestinians' belief that Israel only responds to force. If Hamas extracts border concessions from Israel, this would further discredit Abbas, the most prominent Palestinian proponent of non-violence and of negotiating the terms of a Palestinian state alongside Israel.
Faced with Hamas' rising popularity, Abbas' security forces -- who for years had clamped down on the Islamists in the West Bank -- were forced to stand back this week when demonstrators raised green Hamas banners for the first time in years.
With Hamas doing the fighting and the negotiating, Abbas and prospects for a two-state solution to the Mideast conflict "are on the losing end," said the International Crisis Group think tank.
The Israeli offensive, added Washington-based analyst Jonathan Alterman, may have "provoked one of the more profound shifts in Palestinian politics."