Prime Minister Benjamin Netanyahu plans to convene his security cabinet on Thursday to discuss expanding Israel’s military campaign into the rest of Gaza, even amid growing domestic criticism that such a step would endanger the lives of Israeli hostages held by Hamas and other armed groups in the enclave.

Mr. Netanyahu’s high-stakes proposal comes as the last military operation, which began in mid-March, has come to a virtual standstill and as negotiations with Hamas for a cease-fire and a hostage-for-prisoner exchange have reached an impasse.

A hunger crisis in Gaza, which many aid agencies and foreign governments blame on Israeli policies, has spurred an international diplomatic backlash against Israel, including from some of its closest traditional allies.

In Israel, the proposal to extend the military takeover of the enclave into the heart of Gaza City and central areas of the territory, where officials believe hostages are being held, is causing growing concern, especially among the families of the hostages and their supporters.

After two brief cease-fires and some rescue missions, 50 hostages remain in the enclave, of whom 20 are believed to be alive, according to Israeli officials.

The military says it already controls more than 75 percent of Gaza. Polls have shown that most Israelis want the war to end in a deal that would see the hostages released. But the Israeli government’s stated goal of “total victory” over Hamas has yet to be achieved.

“Hamas’s refusal to release the hostages obligates us to take additional decisions regarding the way to advance the goals of the war,” Israel Katz, Israel’s defense minister, said in a statement on Wednesday.

He listed those goals as “eliminating Hamas while creating the conditions for the hostages’ release and ensuring the safety of the Israeli communities,” meaning those near the Gaza border.

Mr. Netanyahu’s office told some Israeli reporters this week that he was discussing expanding the military campaign into the rest of Gaza, including areas where the hostages are thought to be held. The prime minister’s office said the military was opposed to maneuvering in those areas for fear of endangering the hostages.

But officials briefed on the government’s thinking said that no final decision had been made, and some Israeli analysts said that the proposal may be meant as a threat to try to pressure Hamas into making concessions for a deal.

Hamas has said it won’t agree to a deal without firm guarantees that the war will end. Israel is conditioning any end of the war on the group disarming, a demand Hamas has rejected so far.

Far-right members of Mr. Netanyahu’s governing coalition have been pressing for a full Israeli occupation of Gaza to pave the way for renewed Jewish settlement there 20 years after Israel withdrew its forces and settlers from the enclave. Mr. Netanyahu relies on their support to remain in power.

On Tuesday, thousands of Israelis protested around the country against the government’s plans to expand the fighting and take over all of Gaza.

“We will not allow the hostages to be sacrificed on the alter of a forever war — there must be a deal now,” the Hostages and Missing Families Forum, a grass roots organization that has advocated for the captives and their families, said in a statement.

About 1,200 people were killed in the Hamas-led Oct. 7, 2023 attack on Israel, which ignited the war, and about 250 more were taken to Gaza, according to the Israeli government.

Videos released over the weekend showed two living captives looking emaciated and frail, shocking many Israelis and raising questions about how much longer the men could survive.

More than 60,000 Palestinians have been killed by Israel’s counteroffensive in Gaza, including thousands of children, according to Gaza health officials, who do not distinguish between civilians and combatants. Most of the enclave’s two million residents have been displaced, often more than once, and much of the territory has been reduced to rubble.