It is hard to foresee an imminent breakthrough unless one side crosses the red lines that they have consistently set since the final weeks of 2023. 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, the families of Israeli hostages held in Gaza are no closer to seeing their loved ones. In Gaza, Palestinian civilians face growing hardship from continuing Israeli airstrikes, mass displacement, widespread food shortages and a chaotic start to a new Israeli-backed aid distribution scheme. On Monday, the Israeli military issued new displacement orders for a large area of southern Gaza, effectively ordering civilians to withdraw to a narrow sliver of territory next to the coast.

More than 4,000 Palestinians have been killed in Gaza since Israel resumed fighting in March, according to the Gaza health ministry, which does not differentiate between civilians and combatants. Munir al-Bursh, a director-general of the Gazan health ministry, said in a television interview that at least 10 more people were killed on Monday in a strike on his sister’s home in Jabaliya, northern Gaza. The Israeli military, which often targets Hamas members when they are at home surrounded by relatives, said that it had struck several “terror targets” in the area on Monday but that it could not provide further details on specific attacks without being provided with precise coordinates of the incident.

On both sides, internal dynamics could prove decisive in shaping what happens next. Growing dissent against Hamas could encourage the group to agree to a temporary truce to shore up its short-term control over Gaza. A rise in looting, as well as Israel’s assassination of key Hamas leaders, have highlighted the group’s weakening grip on the territory.

In Israel, Mr. Netanyahu’s coalition could collapse if he agrees to end the war. But it is unclear if he can drag out the conflict indefinitely. The Israeli military is mainly staffed by reservists who have spent much of the last 20 months away from their day jobs and families.

Many of them are exhausted and, if the war continues, there are growing concerns that a significant number will refuse to serve as often or for such long stretches. That would make it hard for Israel’s military leadership to staff ground operations, let alone implement a full occupation that would require tens of thousands of troops to sustain.

Reporting was contributed by Adam Rasgon , Abu Bakr Bashir , Johnatan Reiss , Aaron Boxerman and Rawan Sheikh Ahmad .