BOTH THE Israeli and the Palestinian political systems were locked in bitter impasses during the past month, even as the Biden administration held the Middle East at arm’s length. So it’s not surprising that the worst conflict in years has erupted between the two peoples, with Palestinian missiles raining down on Israeli cities and airstrikes rocking the Gaza Strip.

The trouble started with street unrest in Jerusalem, where Palestinian protests over evictions, Muslim commemorations of Ramadan and an Israeli holiday celebrating its capture of the city overlapped. Under normal circumstances, it might have petered out. But the Islamist Hamas group, which last month was denied an opportunity to take over leadership of the Palestinian movement when secular rival Mahmoud Abbas postponed a promised election, sought to accomplish the same end by other means — firing rockets at Jerusalem and deliberately crossing an Israeli red line.

That, in turn, handed a chance to Israeli Prime Minister Benjamin Netanyahu, who had just failed to form a new government following elections in March and was facing the loss of his office after the past 12 years in power. He quickly vowed to strike back hard, and Israeli planes were soon bombing hideouts and arsenals in Gaza of Hamas and the Islamic Jihad. Three of the latter’s top commanders were killed — but so were a number of civilians, including, by late Tuesday, 10 children, according to Palestinian accounts. Three Israelis died as Hamas indiscriminately targeted Israeli cities with hundreds of rockets.

No one on either side stands to benefit from the fighting, other than the feuding political leaders. Hamas is likely hoping to complete the discrediting of the 85-year-old Mr. Abbas and force him from office. It may also seek to advance a key objective of its ally Iran by disrupting the newly established relations between Israel and several Sunni Arab states. For his part, Mr. Netanyahu might gain from the complication of ongoing negotiations by his political rivals to form a new government, which if successful would leave him with no way to escape prosecution on corruption charges.

Multiple previous conflicts between Israel and Hamas, and two uprisings in the West Bank, have established that neither side can hope for a decisive military victory, or even meaningful political gains over the other. The bloodshed will almost certainly end, sooner or later, with another truce brokered by Egypt, which was working on it Tuesday.

The Biden administration should do its best to support Cairo’s mediation. But it would be wise to resist the inevitable calls for the United States to “reengage” with the long-moribund Israeli-Palestinian “peace process.” As the Obama administration discovered, there is no chance for a breakthrough as long as Palestinians are polarized between Hamas and Mr. Abbas’s secular Fatah movement, and Israeli politics are dominated by Mr. Netanyahu. Before there can be an Israeli-Palestinian breakthrough, both sides must undertake a political renovation. Unfortunately, the new eruption of fighting could make that desperately needed change less rather than more likely.

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