The Israeli government is deeply divided over the ongoing war in Gaza, as highlighted this week by Defense Minister Yoav Gallant's public demand for a clear strategy from the country's Prime Minister Benjamin Netanyahu.

As troops resumed attacks on Palestinians, Gallant voiced his refusal to establish a military "government" in the enclave, underscoring growing Israeli security establishment concerns about the likelihood of post-conflict Israeli rule of Gaza.

This split became more pronounced with the contrasting views of centrist former generals Benny Gantz and Gadi Eisenkot, who supported Gallant, against the far-right nationalist religious factions led by Finance Minister Bezalel Smotrich and Internal Security Minister Itamar Ben-Gvir, who criticized his stance.

"That's no way to run a war," the right-wing Israel Today tabloid headlined its Thursday edition over a photo of Netanyahu and Gallant facing in different directions.

Apart from dismantling Hamas and returning some 130 hostages still held by the group, Netanyahu has not articulated any clear strategic goal for the end of the campaign, which has killed some 35,000 Palestinians, mostly women and children, and left Israel increasingly isolated internationally.

However, backed by Ben-Gvir and Smotrich, both close to the West Bank settler movement, he has rejected any involvement in running postwar Gaza by the Palestinian Authority, set up under the Oslo interim peace accords three decades ago and generally seen internationally as the most legitimate Palestinian governing body.

Netanyahu, struggling to hold his increasingly fractious coalition together, has so far stuck to his pledge of the increasingly unlikely "total victory" over Hamas.

Afterward, Gaza could be run by a "non-Hamas civilian administration with an Israeli military responsibility, overall military responsibility," he mused in an interview with CNBC television on Wednesday.

Israeli officials have said that Palestinian clan leaders or other civil society figures may be recruited to fill the void, but there has been no evidence that any such leaders, able or willing to replace Hamas, have been identified, and no friendly Arab countries have stepped forward to help.

"From Israel, the options are either they end the war, and they withdraw, or they establish, for all intents and purposes, a military government there, and they control the entire territory for who knows how long, because once they leave an area, Hamas will reappear," said Yossi Mekelberg, an associate fellow with the Middle East and North Africa Programme at Chatham House.

Gallant's refusal to contemplate any form of permanent military government reflects the material and political costs of an operation that could stretch the military and the economy painfully, reviving memories of Israel's yearslong occupation of southern Lebanon after the 1982 war.

Yedioth Ahronoth, Israel's biggest circulation newspaper, quoted a confidential assessment from the defense establishment on Friday which estimated the cost of maintaining a military government in the Gaza Strip at about 20 billion shekels ($5.43 billion) a year, in addition to the costs of reconstruction.

The additional troop requirements would draw forces away from the northern border with Lebanon as well as central Israel and mean a sharp increase in reserve duty requirements, it said.

Taking full control of Gaza would require at least four divisions, or around 50,000 troops, said Michael Milshtein, a former intelligence officer and one of Israel's leading specialists on Hamas.

The likely cost to Israel of a prolonged insurgency was illustrated on Wednesday when five Israeli soldiers were killed by an Israeli tank in a so-called "friendly fire" incident in the Jabalia area north of Gaza City.

Israel's military spokesperson, Rear Adm. Daniel Hagari, said the military's job was to "break down those places where Hamas is returning and trying to reassemble itself," but he said any question of an alternative government to Hamas would be a matter to be decided at the political level.

Although most surveys show Israelis still broadly back the war, that support has been slipping, with more and more prioritizing a return of the hostages over attempting to destroy Hamas. Such incidents may erode support further if they continue.

A taste of the broader social divisions likely to be unleashed has been seen in the long-running dispute over conscripting ultra-Orthodox Torah students into the military, a move backed by Gantz and his allies as well as by many secular Israelis but fiercely resisted by the religious parties.

Netanyahu has so far managed to avoid a walkout by either side that could potentially bring his government down.

But Gallant, who has already led a revolt against Netanyahu from within the Cabinet over plans to cut the power of judges last year, has clashed repeatedly with the far-right Smotrich and Ben-Gvir, and his latest challenge to the prime minister may not be his last.