Israel’s three-member unity war Cabinet was formally dissolved Monday, sparking fresh questions about the government of Prime Minister Benjamin Netanyahu’s increasingly controversial war against Hamas in the Gaza Strip and adding fuel to public calls across Israel for new elections and a new government.

Mr. Netanyahu ended the Cabinet after lengthy infighting over war strategy and priorities and the resignation of former Defense Minister Benny Gantz. The Cabinet had governed Israel’s military operations against Hamas since the Palestinian group’s Oct. 7 terrorist attack on Israel.

Mr. Gantz, a centrist and political rival of Mr. Netanyahu, had publicly criticized the government for failing to articulate a plan for postwar Gaza and lacking a clear plan to rescue the remaining Israeli hostages held by Hamas.

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The move removes political cover for Mr. Netanyahu as he fends off global criticism of the situation in Gaza and leaves him dependent for now on hawkish right-wing and religious political allies to stay in power. That may amplify his problems with the Biden administration and other allies.

Mr. Gantz’s exit left only Mr. Netanyahu and Defense Minister Yoav Gallant as members of the war Cabinet.

Right-wing Israeli lawmaker Itamar Ben-Gvir reportedly lobbied to take Mr. Gantz’s place, but such a move likely would have further inflamed tensions with the West and may have signaled that Israel was pursuing an even more aggressive strategy to crush what remains of Hamas’ militant wing battling Israeli troops in Gaza.

The Biden administration is frustrated and publicly critical of Israel for civilian casualties in Gaza and may have viewed the inclusion of hard-liners in the war Cabinet as the final straw.

“Right-winger Itamar Ben-Gvir wanted to take Gantz’s place. That would have effectively destroyed whatever is left of the relationship between Bibi and Biden,” Jonathan Schanzer, senior vice president for research at the Foundation for Defense of Democracies, said during a virtual briefing Monday, using Mr. Netanyahu’s widely used nickname. “So Bibi just blew up the entire thing, with the goal of making war decisions after private consultations with trusted advisers.

“It all sounds pretty chaotic to me, and I continue to harbor serious doubts about the prime minister’s ability to lead.”

Nimrod Goren, senior fellow for Israeli affairs at the Washington-based Middle East Center, said the war Cabinet, formed days after the Oct. 7 Hamas attack, outlived its original purpose to provide “reassurance for the Israeli public amid an unprecedented crisis.”

“With time,” he wrote in a Monday commentary, “this special cabinet increasingly became a facade of responsible wartime management and an enabler for the prime minister. Netanyahu was advancing his own will, while sidelining and sometimes even bashing his centrist coalition partners in the unity government.”

Mr. Goren said he did not expect “dramatic change” in Israel’s war plans with the move, with National Security Adviser Tzachi Hanegbi and Strategic Affairs Minister Ron Dermer continuing to be major influences on the prime minister.

Israeli media reported that the new iteration of Israel’s wartime decision-making body would exclude Mr. Ben-Gvir and other right-wing figures, presumably because of Mr. Netanyahu’s understanding that bringing them into the fold would be politically untenable.

Dissolution of the war Cabinet may have been the only viable option, but specialists say it’s not without consequence. Immediately after the announcement, thousands of Israelis demonstrated in Jerusalem and called for new elections. Key lawmakers stated flatly that a new government is the only answer.

Mr. Netanyahu is facing pressure from all sides. With right-wing officials such as Mr. Ben-Gvir pushing for a tougher stance in the war against Hamas, Mr. Netanyahu also faces pushback from centrists. Knesset member Moshe Tur-Paz of the Yesh Atid party told The Times of Israel that “we have to go to elections and change the government.”

Crucial moment

The political chaos comes at a crucial moment in Israel’s war against Hamas. Israeli troops appear mired in the southern Gaza city of Rafah, home to tens of thousands of Palestinian refugees, but a city that Israeli military officials insist is home to a substantial number of Hamas fighters based in a network of tunnels. Many of the surviving hostages from the Hamas Oct. 7 rampage are thought to be held in the city as well.

Israel faces immense public pressure, including from the U.S., to pause its operations in Rafah and across Gaza and instead pursue a lengthy cease-fire with Hamas. Right-wing figures in Israel oppose such a cease-fire and have threatened to bring down Mr. Netanyanu’s government if it agrees to one.

Negotiations between Israel and Hamas over a truce appear stalled despite an intensive diplomatic push from the Biden administration.

On the northern border, Hezbollah has launched hundreds of rockets and missiles toward Israel over the past several days. Analysts generally agree that Hezbollah is much more dangerous, with a better-armed and better-trained force, than Hamas.

Late Sunday, Israel Defense Forces officials vowed to protect Israeli citizens from Hezbollah.

“Hezbollah’s increasing aggression is bringing us to the brink of what could be a wider escalation — one that could have devastating consequences for Lebanon and the entire region,” IDF spokesman Rear Adm. Daniel Hagari said in a video posted to social media. “Israel has a duty to defend the people of Israel. We will fulfill that duty.”

Israeli military officials said they killed a key operative in Hezbollah’s rocket and missile department, Mohammed Ayoub, in a drone attack Monday morning, potentially dealing a significant blow to the group’s operations.

The risk of a full-blown Israel-Hezbollah war is still at arguably its highest level since Oct. 7. U.S. special envoy Amos Hochstein traveled to Israel and met with Mr. Netanyahu and other key Israeli officials.

Mr. Hochstein met separately with Mr. Gallant, and the two “discussed the security situation at length and its impact on the region,” according to Israeli media.

Mr. Gallant did not attend the meeting between Mr. Hochstein and Mr. Netanyahu, according to a list of participants released by the prime minister’s office.

• This article is based in part on wire service reports.