Prime Minister Benjamin Netanyahu said on Thursday that the Israeli military would keep striking Hezbollah militants in Lebanon with “all our might,” even as the United States, its European allies and several Arab states worked furiously to negotiate a three-week cease-fire.

Mr. Netanyahu’s comments came as he arrived in New York ahead of a planned speech to the United Nations General Assembly, where world leaders have been issuing urgent calls for cease-fires in the Gaza Strip and Lebanon, warning of the risk of a wider Middle East war.

Despite those warnings, Israel said on Thursday that it had killed another high-ranking Hezbollah commander in a bombing in Beirut and had struck Hezbollah targets elsewhere in Lebanon after the militant group, which is backed by Iran, fired 45 rockets into northern Israel. None of them caused damage or injuries.

The Israeli military said it had also bombed a school compound being used as a shelter in Gaza, which it said housed a Hamas command-and-control center. It was the latest in a series of Israeli strikes on former schools. Palestinian Civil Defense officials said 15 people, including women and children, were killed and dozens of others were wounded.

Early Friday morning in Israel, Mr. Netanyahu’s office issued a statement saying: “Earlier this week, the United States shared with Israel its intention to put forward, together with other international and regional partners, a cease-fire proposal in Lebanon. Israel shares the aims of the U.S.-led initiative of enabling people along our northern border to return safely and securely to their homes. Israel appreciates the U.S. efforts in this regard because the U.S. role is indispensable in advancing stability and security in the region.”

The statement said Israeli officials discussed the U.S. initiative on Thursday and “will continue those discussions in the coming days.”

Hezbollah has not responded to the cease-fire proposal, which analysts said would be hard for either side to accept because it falls short of their conditions for a truce.

Hezbollah has said it will not stop firing rockets, missiles and drones at Israel until there is a cease-fire in Gaza. Pausing its own attacks while Hamas fights on could expose Hezbollah to criticism from its supporters that it was abandoning an ally, as well as its principles. Hezbollah began firing into northern Israel on Oct. 8, a day after Hamas led the deadly raid on southern Israel.

Israeli leaders have said they are determined to both crush Hamas and stop Hezbollah from firing on Israel, so that approximately 60,000 displaced Israelis can return to their homes near the Lebanese border. In Lebanon, more than 500,000 people have been forced from their homes by Israel’s counterattacks.

On Thursday, the Israeli military said it had killed another senior Hezbollah commander, Mohamed Hussein Sarour, in an airstrike in Beirut. Hezbollah later confirmed that he was dead. Lebanon’s health ministry, which does not distinguish between civilians and fighters, said at least 92 people were killed on Thursday.

The Israeli military said that Mr. Sarour had overseen the manufacture of Hezbollah’s drones in southern Lebanon, played a role in intelligence gathering, and acted as an emissary to Yemen, where Houthi militants backed by Iran have also launched aerial attacks on Israel.

Israel escalated its assault on Hezbollah last week, blowing up hundreds of its pagers and walkie-talkies and launching a heavy bombing campaign that has killed hundreds and spread fear and panic throughout Lebanon. On Thurs day, the Israeli military released a video of an Air Force commander, Maj. Gen. Tomer Bar, telling soldiers that Israel was preparing for a possible ground invasion in Lebanon.

In a sign of world sentiment, Mahmoud Abbas, the president of the Palestinian Authority, which partly administers the Israeli-occupied West Bank, was greeted by sustained applause when he took the podium at the U.N. General Assembly on Thursday. When he was done speaking, he received a standing ovation.

“Stop the genocide; stop sending weapons to Israel,” Mr. Abbas said in his address. “This madness cannot continue. The entire world is responsible for what is happening to our people in Gaza and the West Bank.”

The proposal for a 21-day cease-fire between Hezbollah and Israel, which was announced by the White House on Wednesday night, has been endorsed by Australia, Canada, the European Union, France, Germany, Italy, Britain, Japan, Saudi Arabia, the United Arab Emirates and Qatar.

The White House press secretary, Karine Jean-Pierre, said on Thursday that President Biden had not spoken to Mr. Netanyahu about the proposal. Calling the violence on the Israeli-Lebanese border “intolerable,” she expressed deep frustration at the lack of progress.

“We felt comfortable releasing that statement last night because we have been having those discussions with Lebanon and Israel,” she said. But she said that it was “up to the parties to respond.”

To compromise to the extent Israel seeks, Hezbollah might need approval from its benefactor, Iran, analysts said.

An ambiguous speech this week to the General Assembly by the Iranian president, Masoud Pezeshkian, could be interpreted as a potential shift in Iran’s stance, said Paul Salem, a senior analyst at the Middle East Institute, a Washington-based research group. In that address, Mr. Pezeshkian condemned Israel’s “desperate barbarism” in Lebanon and called on world leaders to stop Israel’s campaign “before it engulfs the region and the world.”

It is possible, Mr. Salem said, that Iran was giving Hezbollah an off-ramp.

“I can imagine them saying: ‘Look, you know, you’ve done well. You’ve done it for a year. Stand down,’” he said.

Julien Barnes-Dacey, the Middle East and North Africa program director at the European Council on Foreign Relations, said any cease-fire proposal would be Israel’s to scuttle.

“Iran would very much welcome a cease-fire and is desperate to avoid Hezbollah or itself being sucked into a devastating direct war with Israel, so it is really counting on the West to press Israel toward a cease-fire,” he said.

Lloyd J. Austin III, the American defense secretary, pushing for the cease-fire proposal on Thursday, warned of the risk of an “all-out war” in the Middle East that could be “devastating for both Israel and Lebanon.”

“Israel and Lebanon can choose a different path,” Mr. Austin said in London, where he was meeting with his British and Australian counterparts. “All parties should seize this opportunity.”

Reporting was contributed by Ephrat Livni, Aryn Baker, Sheryl Gay Stolberg, Leily Nikounazar, Adam Rasgon, Matthew Mpoke Bigg, Johnatan Reiss, Michael D. Shear, Euan Ward and Stephen Castle.