Eleven days ago, the C.I.A. director, William Burns, arrived in Cairo to join the negotiations over Gaza, which have also been brokered by Qatar and Egypt. Since then, ordinary Israelis began checking their phones every couple of hours to find out the fate of the “iskah,” Israel’s never-quite-consummated ceasefire deal with Hamas. Last Tuesday, we found out, instead, that the Israel Defense Forces had conducted air strikes in part of Rafah, and gained control of the Palestinian side of the land crossing into Sinai, near the Egyptian border. As the country marks an unusually vexed Independence Day, it is not yet clear how the Rafah incursion will affect the negotiations. It is clear that, as the Biden Administration (and many Israeli security experts) conceive it, a deal would not just secure the return of hostages but gesture toward a turning point in the war and in the region—which the Netanyahu government continues to resist.

Netanyahu claims that beneath Rafah, in a network of tunnels and bunkers, four Hamas battalions remain intact, presumably joined by fighters fleeing the north and holding an unknown number of surviving hostages. (Unnamed Israeli officials suspect that many Hamas fighters, along with the leader Yahya Sinwar, have actually moved back to tunnels further north.) Above ground in Rafah, a million Gazan refugees languish in tents, with few facilities and little food. Most are from Gaza City and Khan Younis, where, during the winter, the I.D.F. scattered most other Hamas battalions and, in the process, killed tens of thousands of civilians, and destroyed or damaged half the homes and more than three-quarters of the schools. More than three hundred thousand people are reportedly on the move again, desperately seeking safe zones. When Israeli officials speak of applying military “pressure” to secure the hostages’ release, the implication is that Hamas must believe that an attack on them is imminent; paradoxically, though, Hamas must know that Israel knows that an actual attack would doom the hostages—and, in the eyes of the world, the nation. In any case, it would certainly mean that thousands more Gazan civilians would be killed or subject to famine, which is why the White House firmly opposes an attack. Early last week, President Biden announced that he had held up a shipment of bombs that, he said, “have been used historically to deal with Rafah, to deal with the cities.”

As for the framework for the deal, which the United States supported, it would reportedly involve multiple phases. First, a temporary ceasefire of several weeks would halt the fighting and release “hundreds” of Palestinians in exchange for thirty-three hostages: women, older men, the sick, and the wounded. In addition, Israel would permit Gazan civilians to return to the northern cities, and enable an increase of an unspecified amount of humanitarian aid. It has also been reported that a second phase would aim for an “arrangement to restore sustainable calm.” Then, presumably, the remaining hostages—including those who have died—and Israeli soldiers held by Hamas would be released, in return for more Palestinian inmates in Israeli prisons.

Last Monday, in what appeared a breakthrough, Al Jazeera reported that Hamas had “accepted” the deal. (Israel has called the news agency, which is sponsored by Qatar, a mouthpiece for Hamas, and last week ordered its broadcasting equipment to be confiscated and access to its Web site blocked.) Across Israel, demonstrations led by families of the hostages, calling for the government to bring them home, gained momentum. However, it was soon evident that Hamas had written new language into the draft, such that the first release of hostages might include dead hostages. Hamas also rejected any Israeli veto over which Palestinian prisoners will be freed (which meant that some notorious Hamas leaders could be returned to the West Bank, according to an analysis by the Israeli journalist David Horovitz) and set conditions for Israeli overflight of Gaza.

These were serious changes but also distractions. Irreconcilable approaches to the duration of the second phase would anyway preëmpt an agreement over the first. Hamas claimed that, during the second phase, the ceasefire would, in effect, become permanent, and suggested that it had secured an American guarantee that the war would end after the first phase was complete. (This was consistent with the Biden Administration’s stated aim that “an initial six-week ceasefire would be built into something more enduring.” The Administration did not respond to a request for comment.) Accordingly, Hamas has set conditions that would give it back control of Gaza and gain it more influence in the West Bank, Horovitz wrote. Israel’s Prime Minister, Benjamin Netanyahu, meanwhile, speaks of “absolute victory,” and says that the I.D.F. will go after Hamas in Rafah, deal or no deal. His close allies—Likud populist nationalists, settler messianists, and the ultra-Orthodox—have made clear their intention to fend off any compromise of their claim to the whole “Land of Israel,” which means the West Bank, though not, historically, Gaza. Netanyahu insists that, if he takes the deal, Hamas would “rebuild their military infrastructure” and live to kill another day. His implicit counteroffer is just a turnabout: give me the hostages and I won’t kill you today, but I will as soon as I have them. For now, the stalemate persists.

Or does it? For months, Secretary of State Antony Blinken has been publicly urging Israel—most recently in Riyadh, on April 29th—to consider how its military actions in Gaza might be tempered by the prospect of joining a U.S.-led regional alliance against Iran; how Hamas might be preëmpted by a larger diplomatic plan, including the normalization of relations with Saudi Arabia, rather than by a war of attrition, which would only promise Gazans more carnage and Israel international isolation. In Riyadh, Blinken asked what is to be done, after a ceasefire is in place, about security, governance and administration, and humanitarian and reconstruction needs in Gaza. Right now, Hamas fighters simply reappear where the I.D.F. retreat, prompting Israeli counter-insurgency raids, such as the one in March on the Al-Shifa hospital, in Gaza City, where Israel said Hamas had regrouped. “It’s clear,” Blinken said, “that in the absence of a real political horizon for the Palestinians, it’s going to be much harder, if not impossible, to really have a coherent plan.”

What Blinken was implying is that you have to try to solve the whole puzzle in order to have a shot at solving this part. The Saudis and the Gulf states have the resources to rebuild Gaza, but the Saudis cannot move on close coöperation, let alone normalization, with Israel without an end to the war and an agreement on a clear path to a Palestinian state. Nor can the Saudis, Emiratis, Jordanians, or Egyptians move on any public military alliance. (“They don’t trust Bibi,” the veteran Haaretz security correspondent Amos Harel told me.) Even a preliminary calm would require a Palestinian administration blessed by the Palestine Liberation Organization; the pollster and analyst Khalil Shikaki, who is based in Ramallah, told me that the P.L.O. remains “the only big-tent Palestinian entity that still has broad legitimacy.” And there can be no such blessing without a clear promise of a Palestinian state. (The Saudis, Tom Friedman reported in the Times, would expect a freeze on Israeli settlement construction in the West Bank and a “three-to five-year ‘pathway’ ” to establish a Palestinian state.)

After the early hours of April 14th, moreover, when Iran attacked Israel with three hundred and thirty drones, cruise missiles, and ballistic missiles, the alliance was no longer hypothetical. According to the Intercept, the U.S.—supported by the U.K., French, and Jordanian air forces—shot down more of Iran’s missiles than Israel did. (Other reporting also indicated the use of Emirati and Saudi intelligence.) The few that got through did minimal damage. Nevertheless, Israelis awoke the next morning to a country that seemed, however subtly, changed; even career hawks who, eliding the question of Palestine, once spoke solemnly about Israel going it alone against Iran were now speaking solemnly about the need for an alliance and an openness to a renewed peace process.

“Our first priority is to close any gaps with the Americans,” Moshe Ya’alon, a former Likud defense minister, told the television station Channel Twelve. “This can be done by accepting” Blinken’s proposal, Ya’alon said, “which speaks of a regional alliance, including all the moderate states.” Uzi Arad, a former head of Netanyahu’s National Security Council, told me that the Biden Administration “is asking us to move more constructively on the Palestinian issue. This is in our interest anyway.” Shlomo Brom, a former head of military intelligence, concurred. “The first step in promoting this alliance,” he told me, is “a clear Israel commitment to a political process with agreement on the end goal—and the end goal is a two-state solution. There is no other end goal.”