The death of Mr. Naameh, which Israel’s military confirmed in a statement, was the latest in a string of Israeli killings of Hezbollah commanders in Lebanon, one of which led to an escalation in cross-border exchanges of fire last month that the Biden administration has since battled to contain. With tensions already high, analysts warned that the tit-for-tat strikes could trigger a further escalation and risk open war.

Amal Saad, a lecturer at Cardiff University who researches Hezbollah, said that although the powerful militia was unlikely to allow itself to be dragged into an all-out war over the killing, recent threats by Israeli officials would not deter Hezbollah from responding with strength.

“I don’t think Hezbollah will downplay this,” said Ms. Saad, adding that the rocket barrage was only “a small teaser of what is to come.”

The border flare-up on Wednesday took place as a top U.S. official was in Paris to discuss with French officials how to defuse the tensions between Israel and Hezbollah. Amos Hochstein, a senior White House adviser who has become the de facto U.S. envoy in the quest to resolve the border conflict, met with Jean-Yves Le Drian, President Emmanuel Macron’s special envoy to Lebanon, according to a person close to the talks, who spoke on the condition on anonymity to discuss sensitive diplomacy.

Lebanon was a French protectorate after World War I, and France still has some influence there. The White House had no immediate comment about Mr. Hochstein’s visit.

The conflict between Israel and Hezbollah has so far remained contained, but as exchanges of cross-border fire have intensified in recent weeks, Israeli officials have spoken publicly of shifting their military focus from Hamas to Hezbollah, a far more advanced military threat.

More than 150,000 people have already been displaced on both sides of the border. If a full-scale war were to break out, analysts say, it would likely prove catastrophic, leaving swaths of Lebanon in ruins, causing Hezbollah to unleash its arsenal of precision-guided missiles on cities across Israel and potentially setting off an even wider regional war. Israel’s military leadership has been pressing for the government to reach a cease-fire with Hamas so that Israeli fighting forces can prepare for the possibility of a war with Hezbollah, according to Israeli security officials.

Israel’s defense minister, Yoav Gallant, said on Wednesday that Israeli forces were prepared to take any action necessary against Hezbollah but that they preferred a diplomatic settlement.

“We are striking Hezbollah very hard every day and we will also reach a state of full readiness to take any action required in Lebanon, or to reach an arrangement from a position of strength,” said Mr. Gallant, according to a statement from his office.

“We prefer an arrangement, but if reality forces us we will know how to fight,” he added.

An Israeli official, speaking on condition of anonymity, said that wide gaps between the sides remained but that Hamas’s response left potential to move forward in the talks. The official declined to offer further details.

In a statement on Telegram on Wednesday night, Hamas said it had “exchanged some ideas” with mediators “aiming to stop the aggression against our Palestinian people.” It did not provide any further details.

For months, Israel and Hamas, alongside mediators including Qatar, Egypt and the United States, were in negotiations over the potential deal, which called for a three-stage truce in Gaza and the release of the remaining 120 living and dead hostages held there. However, wide gaps remained on major issues, and the talks had been largely at a standstill since June.

The main stumbling blocks that need to be resolved center on a major difference: Hamas wants an end to the war and a full withdrawal of Israeli forces, while Israel has vowed to keep fighting until Hamas is destroyed and seeks control over postwar security in Gaza.

According to the two senior officials, the disagreements now largely center on two points, both related to talks on a permanent cease-fire outlined in the three-phase U.S.- and U.N.-backed deal. Those talks would take place during the first phase, a proposed six-week truce, during which some hostages would be exchanged for Palestinian prisoners.

Hamas wants to limit those talks to the number and identity of Palestinian prisoners to be released for each remaining hostage, while Israel wants to leave it open-ended, so more topics could be added into the discussions, according to the two senior officials.

Hamas fears Israel might torpedo the talks by expanding them to deal with other, effectively irresolvable issues, which would allow Israel to continue the war, the officials said. The latest Qatari proposal negotiators offers Hamas three potential alternatives for the talks, according to the two senior officials, though they did not give further details. The U.S.- and U.N.-backed proposal stipulates that if Israel and Hamas cannot reach a deal on a permanent cease-fire before the six-week truce expires, negotiations will continue until they do. The two senior officials said Hamas wanted language that guaranteed Israel could not unilaterally declare that the talks had collapsed and return to battle.

In recent weeks, the United States has pushed Qatar — which hosts Hamas’s political leadership — to pressure Hamas to reach a deal with Israel, according to one of the two officials and a senior Israeli official. Qatar has now begun exerting more pressure on Hamas, said the two senior officials involved in the talks.

For months, Hamas’s and Israel’s demands have appeared irreconcilable, each reflecting their desire to shape the future of postwar Gaza. Hamas officials say they will only agree to a hostage-release deal if Israel commits to ending the war and totally withdrawing from the Gaza Strip, allowing Hamas to maintain its rule of the Palestinian enclave.

For its part, Israel has vowed to end Hamas’s rule in Gaza and destroy its military and governing capabilities. Israeli leaders have said military operations there will likely continue for months while Israeli forces chase down the remnants of Hamas’s forces across the Gaza Strip. Israeli soldiers have fortified a major corridor in central Gaza, appearing to prepare for a protracted struggle.

After President Biden publicly backed the agreement in late May, Prime Minister Benjamin Netanyahu of Israel neither rejected the proposed agreement nor issued a full-throated endorsement. Two senior members of Mr. Netanyahu’s far-right government publicly suggested they could break with his coalition if he went ahead with the deal.

But in mid-June, Hamas demanded revisions, and Israel quickly declared that Hamas had rejected the deal, while the Biden administration agreed that some of Hamas’s demands were unworkable.

Last month, Mr. Netanyahu also said in a television interview that he would only accept a “partial deal” with Hamas to release some hostages but would not countenance a premature end to the war. After fierce criticism from the families of Israeli hostages, Mr. Netanyahu publicly endorsed the deal the following day.

Ephrat Livni contributed reporting.

The legalization of the outposts will allow them to grow under Israeli law. Along with far larger and longer established Israeli settlements — all of which are considered illegal under international law — they carve into Palestinian territory that would be needed in any two-state solution.

Palestinians have long argued that the settlements are a creeping annexation, enforced by armed settlers, that is steadily pushing Arabs out of their homes and off their farms.

Israel has made other recent moves to take chunks of West Bank territory. Last week, an Israeli ministry approved the largest seizure of West Bank land since the Oslo Accords in 1993, according to Peace Now, an Israeli group that monitors settler activity. The appropriation, announced on June 25, covered about five square miles of land in the Jordan Valley. As of July, Israel has seized roughly nine square miles of the territory this year, making 2024 by far the peak year for appropriations, Peace Now said.

Mr. Smotrich is a longtime settler activist who has vowed to legalize a new Jewish outpost in the West Bank for every nation that recognizes a Palestinian state. And he indicated that the five outposts, whose legalization he negotiated, were a response to the formal recognition by Spain, Ireland, Norway, Slovenia and Armenia of an independent Palestinian state in recent months.

While building and expanding the settlements is a major aim of far-right members of Prime Minister Benjamin Netanyahu’s governing coalition, the practice has caused conflicts among branches of the Israeli state. Security forces responsible for dismantling illegal outposts have struggled with settlers.

That was the case on Wednesday, when the Israeli military said in a statement that clashes had broken out at a “recently constructed” illegal outpost near Givat Assaf, one of the five scheduled for legalization.

“Masked Israelis” attacked the car of a Civil Administration officer and smashed the windows, the military said. The settlers also hurled a Molotov cocktail at a military vehicle.

Gen. Herzi Halevi, the military’s chief of staff, condemned the clashes and called for the attackers to be punished. “The law must be quickly and swiftly exacted upon the rioters who attacked the security forces as they attempted to carry out their mission,” he said.

Mr. Smotrich has not been circumspect about his intention to expand Israeli’s claim on West Bank territory. In a post on social media on Wednesday, he said he was meeting with the planning authorities to discuss the approval of 5,000 more housing units in Israeli settlements in the West Bank.

“We’re building the good country and thwarting the creation of a Palestinian state,” he said.