Before examining the pitfalls and weaknesses of the Gaza cease-fire, let us welcome even the least of what it may achieve. Fifteen months after the horrendous Hamas attack on Israel and the launch of Israel’s retaliatory invasion, Gaza is a moonscape, most of its 2 million inhabitants homeless, hungry and in despair, and those hostages who are still alive, in the cruel hands of Hamas terrorists, have been torn from their loved ones simply too long. Even the release of only some of the hostages, and even a few weeks of unrestricted humanitarian assistance into Gaza, is good news.

The deal is a tribute to the many months of relentless efforts by the Biden administration and mediators from Egypt and Qatar, and an 11th-hour push from Donald Trump. Debates have already erupted over who deserves credit for finally achieving a cease-fire and who is to blame for delaying it so long, but the incontrovertible fact is that the United States still holds powerful sway over events in the Middle East — including the fate of this agreement, which will require huge effort.

The agreement calls for three phases, of which only the first is described in detail. The initial stage is to last six weeks, during which 33 hostages — women, men over 50, the sick and the wounded — and several hundred Palestinian prisoners are to be exchanged. Israel is to allow a surge of aid into the enclave, and Israeli troops are to start withdrawing from population centers. Negotiations on the second, more difficult phase are to begin while the first is being carried out, and are supposed to cover the release of all remaining living captives held by Hamas and more Palestinians held by Israel, and Israel’s “complete withdrawal.” Details of the third phase are unclear, but they presumably will include return of the remaining deceased hostages and prisoners and a reconstruction plan for Gaza. The critical question of who will administer Gaza after the cease-fire also remains unsettled.

That leaves plenty of room for either side to back out, as they have again and again in the negotiations. Phased plans have a dismal record in the Israeli-Palestinian struggle because they are conditioned on each side fulfilling the terms of the current phase, effectively giving zealots on both sides ample opportunity to derail the process, as the fates of Oslo, Oslo II, Hebron, Wye River and so many other “peace processes” bear witness.

Neither the Israeli far right nor Hamas is keen on the deal. For Prime Minister Benjamin Netanyahu and his right-wing followers, the fact that Hamas has not been eradicated is insufferable. And some extreme nationalists — including Finance Minister Bezalel Smotrich and Itamar Ben Gvir, who resigned as national security minister on Sunday over the deal — have not abandoned their ambition to build on Israeli military successes against Hamas and Hezbollah to restore Jewish settlements to Gaza and to annex West Bank territories. Hamas, which rejoiced in the atrocities it committed in Israel on Oct. 7, 2023, and effectively invited the destruction of the territory it purports to lead, will try to use the freeing of large numbers of prisoners to enhance its standing among Palestinians and balk at any deal that further weakens its hold on Gaza.

That puts considerable responsibility on the Trump administration to keep the process on track. President Trump has been widely and properly credited for pushing Mr. Netanyahu into accepting the cease-fire, first by warning in early January that “All hell will break out” if hostages were not released by the time he entered office and then by sending his old friend and new Mideast envoy, Steve Witkoff, to personally lean on Mr. Netanyahu. This enabled the prime minister to tell his right-wing cohort that he had no choice, since the president they so ardently hoped for was not with them on this.

That may not fully justify Mr. Trump’s boast that the agreement was a result of “our Historic Victory in November” — the deal that Mr. Trump pushed over the finish line was essentially the same as what President Joe Biden had proposed last May and might have been adopted in any case. But if Mr. Trump believes he was instrumental in achieving the deal, he should also accept responsibility for sustaining the cease-fire and for its fate.

That does not mean he will. Mr. Trump’s only clear demand on Israel was that the hostages be released in time for his inauguration. The history of his first stint in the White House suggests little sympathy for the Palestinians and no interest in the “two-state solution” that has been the holy grail of American diplomacy for many years. Among Mr. Trump’s first acts after his inauguration was to lift sanctions imposed by the Biden administration on dozens of far-right Israelis and settler groups. And when asked whether he thought the cease-fire would hold, he showed little interest in the conflict. “That’s not our war,” he said. “It’s their war.”

By all accounts, Mr. Trump is far more interested in building on the Abraham Accords his first administration brokered, under which Israel established relations with the United Arab Emirates, and to similarly normalize relations between Israel and Saudi Arabia. He is said to see a Nobel Peace Prize there, and not in the notoriously thankless efforts to settle the Israeli-Palestinian struggle.

Beyond that, he is likely to be as unpredictable and impetuous in his foreign dealings as he was the first time around. Mr. Netanyahu and his far-right allies, and the surviving Hamas leadership, will be watching Washington carefully for signals, and without American pressure the deal will be at great risk.

It will be up to Mr. Trump’s new foreign-policy team — National Security Adviser Mike Waltz, Secretary of State Marco Rubio and Mr. Witkoff — to remind the president that his government bears responsibility for the cease-fire agreement, and to point out that a rekindled war in Gaza and the annexation of any part of the West Bank would most likely undermine Mr. Trump’s ambitions for regional diplomacy.

By contrast, a Gaza at peace and an international reconstruction program there funded by Gulf oil money would be a fitting centerpiece for Mr. Trump’s Middle East project. That would make it easier to establish diplomatic ties between Israel and Saudi Arabia, and that, in turn, would strengthen an American-led alliance to force Iran to the bargaining table.

Such a program is all the more feasible at a time of acute upheaval in the Middle East. Israel is in an unusually strong position: It has effectively defeated Iran’s proxies to its north and south, Hamas and Hezbollah, while the collapse of the Assad regime has rendered Syria largely harmless and has further weakened Iran’s power to threaten Israel. The Gaza cease-fire could also accelerate the end of Mr. Netanyahu’s rule, giving the Trump administration a fresh start with a new, more moderate leadership.

The Middle East, alas, has a way of confounding optimistic scenarios. The return of hostages and the opening of Gaza to caravans of desperately needed food, clothing and medicine are already huge and welcome achievements. The progress need not stop there.