Israel’s leaders have articulated various goals for their expanding ground and air assault in Gaza, spreading confusion over how the objectives might be achieved and on what terms the renewed campaign might end.

They agree on the primary objective — to squeeze Hamas into releasing the dozens of hostages still being held in the enclave, with negotiations at an impasse. On Thursday, the military issued more evacuation warnings for residents of neighborhoods in eastern Gaza City ahead of operations there.

But other goals have since emerged: On Wednesday, Prime Minister Benjamin Netanyahu said that Israel had “moved up a gear” in Gaza, capturing more territory, hitting militants and carving up the coastal strip.

And he also repeated his ultimate goal of crushing Hamas’s military capabilities and terminating the group’s rule there, which hasn’t happened despite over a year of war.

The Israeli defense minister, Israel Katz, said the military was seizing swaths of territory to protect its forces and border towns, suggesting a longer-term presence in the enclave.

And over the weekend, Mr. Netanyahu said Israel would enable what he described as the voluntary emigration of Gazans — again without any clarity about how this would happen, or where they would go.

The uncertainty about what is to come may be the point. Israel’s military chief, Lt. Gen. Eyal Zamir, said during a field visit to Gaza on Wednesday that it would “preserve operational ambiguity and the element of surprise,” adding, “The only thing that can halt our advance is the release of our hostages!”

The forces appear to be gradually dissecting the enclave into separate districts, in part to encircle and restrict the movement of Hamas fighters who have regrouped in certain areas, according to analysts.

But as the military raids areas of Gaza that it had already conquered multiple times before, questions remain about what the forces can do this time that they couldn’t do in 15 months of fighting.

“The government has not yet presented a viable diplomatic framework that will translate the military achievements into realizing the war objectives over time and justify the prices paid for them,” said Assaf Orion, a retired Israeli brigadier general who is now a senior fellow at the Washington Institute for Near East Policy.

Nor is it clear how the campaign will help the hostages who were taken in the Hamas-led attack on Israel on Oct. 7, 2023, which ignited the war, with the group insisting on negotiations as the only way to free them.

Former hostages have testified that their conditions in captivity only worsened as military pressure increased and that they feared being killed at any moment by their captors or Israeli bombardment.

To a large extent, Mr. Orion said of Israel’s renewed offensive, “it is a development that endangers the lives of the remaining hostages.”

A temporary cease-fire with Hamas collapsed on March 18 when Israel launched a deadly air attack after talks to extend the cease-fire stalled.

In the weeks since, Israeli ground troops have retaken the Netzarim Corridor, a route dividing the northern and southern halves of the Gaza Strip.

On Wednesday, Mr. Netanyahu said Israeli forces were seizing another east-west corridor, this one north of one they already control along the Egyptian border.

The military has thickened parts of a buffer zone inside Gaza’s perimeter, has expanded ground raids in the northern and southern ends of the enclave and has issued sweeping evacuation orders. That has led to the displacement of more than 140,000 people in Gaza since the cease-fire broke down, according to the United Nations.

More than 1,000 people in Gaza have been killed since the cease-fire collapsed, according to the Gaza health ministry, which does not distinguish between civilians and combatants.

In another tactic aimed at pressuring Hamas, Israel halted the entry of all commercial goods and humanitarian aid into Gaza a month ago, leading to price gouging by local merchants and to shortages. The World Food Program, a U.N. agency, said it had run out of the flour and fuel needed to keep bakeries in Gaza open.

Gaza health officials say that more than 50,000 people have been killed in the enclave in the war prompted by the Hamas-led attack on Israel that killed about 1,200 people, according to Israeli officials, and in which 250 were taken to Gaza as hostages.