Through nearly 20 months of war in Gaza, a changing carousel of mediators and negotiators have tried — and failed — to reach a lasting truce between Hamas and Israel. William J. Burns and Brett McGurk led the way for the Biden administration, before Steve Witkoff tried on behalf of President Trump.

Whoever the mediator, one intractable dispute has consistently prevented a deal. Hamas wants a permanent cease-fire that would essentially allow the group to retain influence in postwar Gaza. Israel wants only a temporary deal that would allow it to renew its failed efforts to defeat Hamas.

Now, once again, that fundamental difference is the main obstacle to a new truce. After a renewed flurry of mediation from Mr. Witkoff and his team last week, Hamas sought stronger guarantees that any new cease-fire would evolve into a permanent cessation of hostilities.

Though the proposed new deal would officially last for 60 days, Hamas pushed for a clause that guaranteed “the continuation of negotiations until a permanent agreement is reached.” That wording would technically allow for the 60-day cease-fire to be extended indefinitely, scuppering Israeli hopes of returning to battle.

Hamas’s demand drew a familiar response from Israel. “Hamas’s response is totally unacceptable and is a step backward,” Prime Minister Benjamin Netanyahu said in a statement.

This new version of an old dispute has not immediately collapsed the negotiations. Egypt and Qatar, the two main Arab mediators, released a joint statement on Sunday in which they pledged “to intensify efforts to overcome the obstacles facing the negotiations.”

It is hard to foresee an imminent breakthrough unless either side crosses their respective red lines. Israeli officials have suggested they could agree to a permanent truce if Hamas disarmed and its leaders left Gaza for exile. While some Hamas officials have expressed openness to some kind of compromise over their weapons, the group has publicly rejected the premise.

In the meantime, Palestinian civilians in Gaza face growing hardship, amid continuing Israeli airstrikes, widespread food shortages, and a chaotic start to a new Israeli-backed aid distribution scheme. And in Israel, the families of hostages held in Gaza are no closer to seeing their loved ones.

Aaron Boxerman and Rawan Sheikh Ahmad contributed reporting.