As Israel pounded targets in the Gaza Strip from the air and sea on Wednesday, a member of the country’s war cabinet threatened action on a second front, along the border with Lebanon, where the Iranian-backed militia Hezbollah has fired rocket barrages into Israel.

“I say to our friends around the world: The situation in the northern border necessitates change,” the war cabinet member, Benny Gantz, told reporters. “The time for a diplomatic solution is running out. If the world and the government of Lebanon don’t act to stop the fire toward northern communities and to push Hezbollah away from the border, the I.D.F. will do that.” The reference was to the Israel Defense Forces.

The threat of a wider war has preoccupied the United States and its allies since the start of the conflict in Gaza, and has only grown as three Iranian-backed groups — Hamas, Hezbollah and Houthis in Yemen — launch attacks toward Israel as well as on commercial ships in the Red Sea. The concern prompted the United States to dispatch two aircraft carriers to the Eastern Mediterranean in the weeks after the Oct. 7 Hamas-led attacks on Israel that sparked the war in Gaza.

The Israeli military said Wednesday that its northern command, along the border with Lebanon, was in a “state of very high readiness.” The military’s chief of staff, Lt. Gen. Herzi Halevi, said, “We need to be prepared to strike if required.”

Tensions rose even higher this week after Iran accused Israel of killing Brig. Gen. Sayyed Razi Mousavi, a senior adviser to Iran’s Islamic Revolutionary Guards Corps, in a missile strike in Syria. On Wednesday, a cortège of mourners accompanied his body through the Iraqi cities of Najaf and Karbala, and a representative of the Revolutionary Guard, Ramezan Sharif, again threatened retaliation against Israel, The Associated Press reported.

Hints of division among Israel’s adversaries emerged on Wednesday when Mr. Sharif claimed that Hamas’s Oct. 7 attack was prompted not by longstanding grievances with Israel but for the 2020 killing of Maj. Gen. Qassim Suleimani, head of Iran’s elite Quds Force, in a U.S. drone strike in Iraq. Hamas promptly rejected the suggestion.

American officials have been wary that tit-for-tat attacks in the region could escalate into a larger, regional fight, but early on Tuesday, the United States conducted a round of airstrikes in Iraq on facilities it said were being used by Iranian proxies. The strikes followed a series of attacks by the militants in Iraq, including a drone attack hours earlier on an Erbil air base in which three American service members were injured.

An Israeli official said Wednesday that Secretary of State Antony J. Blinken plans to visit Israel in early January to discuss the war in Gaza and plans for how the Palestinian territory will be governed when the conflict ends. The visit will be Mr. Blinken’s fourth to the region since the Oct. 7 attacks. On each of his earlier trips, Mr. Blinken has also stopped in several Arab capitals.

Israel has been under pressure by European governments and the United Nations to agree to an immediate cease-fire, but with Hamas and Israel staking out seemingly intractable conditions in public, diplomats said it appeared that a deal for a lasting truce remained far off.

In Israel on Wednesday, a day after the Israeli military said it had expanded operations in central areas of Gaza, air raid sirens sounded along the border at least three times — a measure of the seeming durability of Hamas’s capabilities to fight and threaten Israel.

Since the Oct. 7 attack on southern Israel, which killed an estimated 1,200 people, Hamas and other armed groups have fired about 12,000 rockets from Gaza into Israel, a quarter of them on Oct. 7, according to the Israeli government. Israel has hit Gaza with a near-relentless barrage of strikes, killing what health officials say is more than 20,000 people.

More than 11 weeks after the Hamas-led attack that set off the war, the Gazan Health Ministry said Wednesday that Israel had returned the bodies of 80 Palestinians to Gaza.

An Israeli official said that Israeli soldiers sweeping Gaza in search of hostages held by Hamas and other armed groups had taken the bodies to Israel to determine if any of them were the remains of hostages. The Israeli authorities then coordinated with Palestinian officials to send them back to Gaza, said the official, who spoke on the condition of anonymity to discuss military operations.

In Gaza, Israeli soldiers were engaged in house-to-house battles in a neighborhood outside Gaza City, where there has been fighting for weeks, the military said. Earlier this week, General Halevi said that the military was “close to completing” the dismantling of Hamas battalions in northern Gaza, but that given the dense urban environment, “it cannot be said that we killed them all.”

The war, he said, “will continue for many more months.”

Since the start of the conflict, both Israel and Hamas have made hard-line statements in public even as talks have continued in private, often through the Qatari government, which brokered a November truce that opened the door to a hostage-for-prisoner exchange and more humanitarian aid entering Gaza.

The Egyptian government has circulated a proposal calling for further exchanges of hostages and prisoners as a step toward a permanent cease-fire, according to three diplomats in the region who insisted on anonymity because of the sensitivity of the talks. But the diplomats cautioned that neither Israel nor Hamas appeared close to agreeing.

On Monday night, Israel’s war cabinet discussed various truce proposals on the table, including the Egyptian one, according to an Israeli official who spoke on the condition of anonymity to discuss the confidential deliberations. In public, Israeli officials have continued to tell the public to expect a long and difficult war ahead.

Hamas, in public statements, has appeared to dismiss any deal to release the remaining hostages if it does not include a sustainable end to hostilities. In an interview with The New York Times on Wednesday, Zaher Jabareen, a member of the group’s political leadership, said the first step had to be an end to the killing of people in Gaza.

“Our position, which we communicated to all the parties, is that we are asking for a comprehensive cease-fire before we talk about other issues,” he said.

Reporting was contributed by Aaron Boxerman, Ben Hubbard, Michael Crowley and Johanna Reiss.