The Ukrainian military is losing ground in eastern Ukraine at the fastest pace in years. An influx of several thousand North Korean soldiers to Russia has added an unpredictable new dimension to the most savage war in Europe in generations.

And Russian bombardments — including 20 nights of drone assaults on the capital, Kyiv, in October alone — add to the civilian casualty count every day.

Against this difficult backdrop, Ukraine is bracing for the U.S. elections on Tuesday that will almost certainly shape the course of the country in profoundly different ways, depending on who wins the White House.

Former President Donald J. Trump, the Republican nominee, and Vice President Kamala Harris, the Democratic nominee, have expressed starkly contrasting visions for America’s role in the war as well as in the NATO military alliance that has long served as a shield against Russian aggression.

Ukrainian officials — desperate to steer clear of the toxic partisan battles that could jeopardize support from their chief military backer — are seeking to find ways to make different arguments that might appeal to both camps.

Mr. Trump’s claim that he will be able to broker a deal to end the war even before he takes office along with his often-expressed dim views of Ukraine — he has even blamed President Volodymyr Zelensky for starting the war — have stoked concerns that he would force the Ukrainians into a bad deal by cutting off military support.

Mr. Zelensky, who is asked about the prospect of a Trump victory in nearly every news conference and media appearance, told journalists in Iceland last week that he “understands all the risks.”

“Trump talks a lot, but I didn’t hear him say he would reduce support for Ukraine,” he said.

At the same time, Mr. Zelensky is under no illusions about the dire consequences of losing U.S. military assistance.

“If that support weakens, Russia will seize more territory, it would prevent us from winning this war,” he told the South Korean broadcaster KBS. “That is the reality.”

Kyiv is clearly looking for ways to appeal to Mr. Trump’s well-documented transactional approach to foreign policy, with Mr. Zelensky emphasizing that helping defend Ukraine is in America’s economic interests since his country “is rich in natural resources, including critical metals worth trillions of U.S. dollars.”

In 2022, the Canadian consulting company SecDev estimated the full value of all mineral resources of Ukraine at $26 trillion, including coal, gas and oil. Strategic resources — including some 7 percent of the world’s titanium reserves, 20 percent of its graphite reserves and 500,000 tons of lithium essential for electric car batteries — are within Ukrainian territory.

Russia is already plundering some of these resources in occupied territories, according to Ukrainian officials, British intelligence and independent investigations.

Those precious resources, Mr. Zelensky said, “will strengthen either Russia and its allies or Ukraine and the democratic world.”

Senator Lindsey Graham, Republican of South Carolina and a Trump ally, made a similar point in a video he recorded with Mr. Zelensky in September. “They’re sitting on a trillion dollars’ worth of minerals that could be good to our economy,” Mr. Graham said. “So I want to keep helping our friends in Ukraine.”

Mr. Zelensky has also mentioned the possibility of using Ukrainian units to replace certain American troops stationed in Europe after the war, noting that battle-hardened Ukrainian troops could prove useful in protecting the European continent.

That may also have been an appeal to Mr. Trump’s longstanding goal of reducing America’s military presence in Europe. In 2020, he withdrew nearly 10,000 troops from Germany — about a quarter of the contingent stationed there.

“Donald Trump is entirely unpredictable — in both negative and positive ways,” said Oleksandr Kovalenko, a prominent Ukrainian military and political analyst. “Trump could very unpredictably take a stance that completely blocks aid to Ukraine, or he could just as unpredictably decide to provide Ukraine with support that neither Joseph Biden nor Kamala Harris would ever consider.”

Ms. Harris is widely seen as more predictable and likely to pursue policies similar to the Biden administration’s, which presents a different set of challenges for Kyiv.

Many Ukrainians believe that the Biden administration has been cowed by fear of a direct confrontation with Moscow, leading to an overly cautious and slow response that ultimately consigns them to a slow defeat.

“A future President Harris would need to deal with a central problem in America’s support for Ukraine: Does it want Ukraine to beat Russia and is it willing to provide the military, diplomatic and financial resources to do so?” Mick Ryan, a retired Australian Army major general and a fellow at the Lowy Institute, a research group, wrote recently.

“If the answer to this question is yes, it will require the United States and NATO to shift their strategy, and will demand a closer alignment of NATO and Ukrainian strategy to see the war through to victory,” he wrote.

Mr. Biden’s tepid response to a plan for victory that Mr. Zelensky presented on a recent trip to Washington has added to a deepening sense of frustration that has spilled into public view, with Kyiv saying it limits its options for finding an acceptable end to the war.

There is no indication that the United States will provide Ukraine with the kind of military support it believes it needs to force Russia into negotiations and no sign that Washington is ready to commit to the kind of security guarantees Kyiv views as essential to a durable peace.

Mr. Zelensky told reporters this week that America had delivered only a small fraction of the military support it pledged in a $61 billion aid package passed in April, complicating Ukraine’s ability to plan for what comes after the presidential election in the United States.

“You have to count on very specific things in very concrete time, otherwise you can’t manage this situation, you cannot manage defending lines, you can’t secure people, you can’t prepare for the winter,” he said this week.

“It’s not a question of money,” he said. “It’s always a question of bureaucracy, logistics, ideas or skepticism.”

As Ukraine continues to lose ground on the eastern front, Mr. Kovalenko, the military analyst, said that no matter who wins on Tuesday, the domestic partisan political battles that could follow the election present their own risk, sowing chaos that Moscow will move to eagerly exploit.

“What actually frightens me more is not January 2025, when the inauguration will take place, but the period right after the election,” he said in an interview. “Russia will now take full advantage of the U.S. elections, after which internal political events will dominate, distracting American society from Ukraine and other foreign policy issues.”

Constant Méheut and Liubov Sholudko contributed reporting from Kyiv.

They came by bus, by tractor or on foot. They waded through mud hoping to help clean up neighborhoods washed away by floodwaters that have killed at least 211 people.

Thousands of Spanish citizens made their way to flood-ravaged Valencia over the weekend after the country’s worst natural disaster in recent history left the nation shocked by images of overturned cars and brick homes torn apart by furious water.

The devastation has become a political flashpoint and brought home fears over the effects of climate change. But for many, the most immediate and important response was to lend a hand.

While the military, the police and civil guard officers searched for survivors and cleared debris, civilians joined in the effort wherever they could, determined to help Valencia and surrounding regions rebuild and to help its citizens recover.

On Saturday, a parade of tractors rolled into urban Valencia, a province on Spain’s eastern shoreline, driven by farmers from around the region who had come to help clear debris. “The countryside is once again showing its solidarity,” Valencia’s agricultural association said on social media.

With major roads in the Valencia province closed to vehicles, many decided to walk, carrying brooms, rakes and buckets, according to footage aired by Spanish broadcasters. A sea of people crossed the bridge to Paiporta, a town where at least 60 people were killed and mud still clogged the streets after a river burst its banks.

In urban Valencia, the city’s celebrated soccer club offered Mestalla Stadium as an emergency center where citizens could drop off bags of food, clothes and bottles of water. City officials and volunteers also set up a food bank, serving food along the stadium’s main entrance.

“The image of Mestalla filled with people coming together, arriving to donate products, and applauding each time a truck leaves full of food and basic necessities, will be unforgettable,” Javier Solís, the club’s corporate director, said.

Alongside star players like José Gayà and Jaume Doménech, fans and volunteers sorted and packed food destined for devastated neighborhoods. Candela Reig Moril, an industrial engineering student who lives in central Valencia, helped coordinate university students who wanted to help, and ended up working with hundreds of people who wanted to do something for their city.

“Many of them come crying because of this huge, unexpected catastrophe,” Ms. Reig Moril, 21, said. “The little children have even come to deliver their toys. It’s very touching to see everybody so willing to show solidarity.”

Volunteers have used social media or message boards set up in response to the disaster to find out how they can help. They have offered beds for displaced families or shelter for pets and have volunteered their professional skills, from logistics management to cooking.

Claudia Orts García, a nursing assistant, used a message board to collect food, medication and feminine hygiene products. On Sunday, she and her partner plan to drive from Dénia, a port town south of Valencia city, to the worst affected areas, where they will deliver the donated supplies. Some friends who also wanted to help have asked to ride along. Ms. Orts García said she will also offer medical assistance where possible.

“We will lend a hand in everything that is necessary,” she said.

Amid the rush to help those in need, there was also a wave of criticism directed at the Spanish government. Parts of Valencia were doused in a year’s worth of rain in just eight hours, and some said government warnings came too late. Other victims said rescue workers and the police took too long to respond to the disaster. Dozens were still missing by Saturday.

For Toni Zamorano, who was trapped on the roof of his car for hours as rain fell, the volunteers have become a lifeline. In the town of Sedaví, houses and businesses were completely flooded. Mr. Zamorano said he has lost everything.

Were it not for the volunteers who work from sunrise to sunset, he would not have clothes, food and water, he said. Not only have the volunteers provided the basic necessities, they have also restored his faith in humanity, he said.

“I feel that humanity is still capable of forgetting its differences. Here, race or economic level don’t matter,” he said. “This solidarity makes you feel great, then you close your eyes when you sleep, you remember everything you have seen and you understand the magnitude of this tragedy.”

When a state-funded Polish radio station canceled a weekly show featuring interviews with theater directors and writers, the host of the program went quietly, resigned to media industry realities of cost-cutting and shifting tastes away from highbrow culture.

But his resignation turned to fury in late October after his former employer, Off Radio Krakow, aired what it billed as a “unique interview” with an icon of Polish culture, Wislawa Szymborska, the winner of the 1996 Nobel Prize for Literature.

The terminated radio host, Lukasz Zaleski, said he would have invited Ms. Szymborska on his morning show himself, but never did for a simple reason: She died in 2012.

The station used artificial intelligence to generate the recent interview — a dramatic and, to many, outrageous example of technology replacing humans, even dead ones.

Mr. Zaleski conceded that the computer-generated version of the poet’s distinctive voice was convincing. “It was very, very good,” he said, but “I went to her funeral, so I know for sure that she is dead.”

The technology-enabled resurrection of the dead poet was part of a novel experiment by Off Radio Krakow, an arm of Poland’s public broadcasting system in the southern city of Krakow. The aim was to test whether A.I. could revive a moribund local station that had “close to zero” listeners, according to the head of public radio in Krakow.

The station also planned from-the-grave interviews with other dead people, including Jozef Pilsudski, Poland’s leader when it regained its independence in 1918.

Novelty value — and a storm of public outrage — worked to bolster Off Radio Krakow’s audience, which the head of Radio Krakow said grew to 8,000 overnight from just a handful of people after the introduction of three A.I.-generated Generation Z presenters — Emilia, 20, Jakub, 22, and Alex, 23, each of whom had a computer-generated photograph and biography on the station’s website.

Less welcome than the audience surge, however, has been a barrage of abuse directed at the public broadcasting system and accusations that it was sacrificing humans on the altar of technology.

“I have been turned into a job-killing monster who wants to replace real people with avatars,” said Mariusz Marcin Pulit, the editor in chief of Radio Krakow and of niche stations operating under its umbrella, like Off Radio Krakow.

He insisted that it was never his intention to replace people with machines, and that his only goal was to revive Off Radio Krakow, make it more appealing to younger listeners and stir debate about A.I. as Poland’s Parliament discusses new legislation to regulate its use.

The technology used to generate the fake interview with Ms. Szymborska and other programing, he added, has been widely used: Open AI’s ChatGPT, speech synthesis software developed by ElevenLabs, and the image-generating programs of Leonardo.Ai.

But his assurances have done nothing to calm public anger — and alarm that humans are being written out of the script.

Among those outraged by Mr. Pulit’s experiment was Jaroslaw Juszkiewicz, a radio journalist whose voice was used for more than a decade to guide drivers using the Polish version of Google Maps. His replacement by a metallic computer-generated voice in 2020 stirred fury on social media, prompting Google to restore Mr. Juszkiewicz, at least for a time.

He announced recently that he had been yanked again, lamenting that A.I. was “sweeping through the world of human voice work like a giant steamroller. And I can, in my own human voice, say, probably for the last time: ‘Smile beautifully and head south.’”

In a Facebook post, he said the use of A.I. to fake an interview with the dead Nobel Prize winner had left him speechless. “If that is not a breach of journalistic ethics,” he said, “I don’t know what is.”

The National Radio and Television Council, a regulatory body stacked with supporters of Poland’s previous right-wing government, assailed Mr. Pulit, who was appointed by a new center-left administration formed in December. He was “eliminating the human factor” and forcing media to obey “unethical commands and ideas serving, for example, strictly political interests,” a council member, Marzena Paczuska, wrote in a letter to the culture minister.

A member of the government also expressed alarm. The minister of digitalization, Krzysztof Gawkowski, complained on the social media platform X that “although I am a fan of A.I. development, I believe that certain boundaries are being crossed more and more.” He added: “The widespread use of A.I. must be done for people, not against them!”

Tired of being accused of wanting to make humans redundant, Mr. Pulit, the head of Radio Krakow, recently pulled the plug on his A.I. experiment.

“We are pioneers, and the fate of pioneers can be difficult,” he said in a recent message to staff members announcing an abrupt termination of A.I. presenters and their replacement by music created and performed by humans.

Among the A.I. presenters removed from Off Radio Krakow was Alex Szulc, a nonexistent person who had been presented as a nonbinary progressive “full of social commitment.” A biography on the station’s website was later rewritten to delete any mention of the presenter’s sexual orientation after angry complaints from L.G.B.T.Q. activists that they needed a real person to speak for them, not a computer-generated one.

Also gone is Emilia Nowak, the station’s computer-generated “pop culture expert,” who conducted the “interview” with the dead poet. The station first announced the conversation as if it were a real interview, but later clarified that it had been fabricated by a machine.

Michal Rusinek, the head of a foundation that manages the late Nobel Prize winner’s literary estate, said he had given Off Radio Krakow permission to use Ms. Szymborska’s voice for the segment because the poet “had a sense of humor and would have found it funny.”

But he said the interview “was horrible” and put words in the poet’s mouth that she would never have used, making her sound “bland,” “naïve” and of “no interest whatsoever.” But that, he added, was heartening because “it shows that A.I. does not yet work” as well as humans. “If the interview had been really good,” he said, “it would be terrifying.”

Felix Simon, the author of a report published in February on the effect of A.I. on journalism, said the Polish experiment had not altered his view that technology “aids news workers rather than replaces them.” For the moment, he added, “there is still reason to believe it will not bring the big jobs wipeout some people fear.”

For the many in Poland who criticize Off Radio Krakow’s flirtation with A.I., the station’s use of computer-generated presenters, though now suspended, has highlighted a grave and immediate danger.

An online petition drafted by Mr. Zaleski, the terminated culture show host, and Mateusz Demski, a fellow presenter who also lost his job, warned that “the case of Off Radio Krakow is an important reminder for the entire industry” and a “dangerous precedent that hits us all.”

The use of A.I.-generated presenters, the petition warned, “is opening the door to a world in which experienced employees associated for years with the media and people employed in creative industries will be replaced by machines.”

Mr. Pulit, the editor in chief, dismissed that as “fake news,” noting that none of the people who had lost their jobs at the radio were full-time employees.

Mr. Zaleski said most of his income had always come from work as a theater director, so he was not particularly upset when he lost his weekly slot on Off Radio Krakow, which paid only $62 per show.

But he said he was appalled at being replaced by a machine-generated substitute. “I was very angry that real, deep talks and real interviews with real people were replaced with something totally fake.”

Anatol Magdziarz contributed reporting from Warsaw.

The patrol begins at dusk every night, as the thuds from nearby artillery echo over the distant hills in southern Lebanon. Some scouts settle into hidden perches on the outskirts of town, keeping close watch on the roads leading into it. Others hop on their motorcycles and roam the streets, alerting the police to any suspicious cars or strangers.

The volunteer force describes itself as the first line of defense in Hasbayya, a mostly Druse and Christian town near the Lebanese-Israeli border. But the volunteers are not scanning for only the Israeli troops who invaded southern Lebanon last month as the conflict between Hezbollah and Israel escalated. They are also trying to prevent Hezbollah fighters from entering the town — and dragging it into the wider war.

The Israel-Hezbollah conflict was once contained to the border region, but has since enveloped swaths of southern and eastern Lebanon, a small Mediterranean country half the size of Vermont. Israeli airstrikes have rained down across the region, leveling beige stone homes and pulverizing villages into rubble. Hezbollah fighters have volleyed rockets back toward Israel and clashed with invading Israeli troops.

Israel’s military campaign has left few communities in the south untouched. Villages in the south where there is deep support for Hezbollah, an Iran-backed Shiite Muslim movement, have been flattened. Other mostly Christian, Sunni and Druse Lebanese towns that do not support Hezbollah have also been hit.

Lebanon has long been deeply divided along sectarian lines, mainly among its three dominant groups — Shiite and Sunni Muslims and Christians. Hezbollah is the most powerful political and military group in the country, representing many Shiites.

While Lebanese people are largely united against Israel’s onslaught, some in southern towns where Hezbollah does not hold sway say they feel trapped in the crossfire between Israel’s firepower and Hezbollah’s fighters. Desperate to shield their communities, some are cobbling together informal defenses of their own.

In Hasbayya, residents have established a neighborhood watch group. Some local leaders have negotiated with Hezbollah to keep its fighters from launching rockets from the town.

Officials within Hasbayya have also turned away Shiite Muslim families displaced from nearby villages where Hezbollah is dominant — a move that risks inflaming sectarian tensions that are always simmering. Local officials said they feared that Hezbollah fighters might be among the families, which could make them — and by extension the town — a target of Israeli strikes.

Locals know that Hezbollah, with its overwhelming military might, could go back on their pledge to steer clear of Hasbayya at any time and the town would be largely powerless to stop them. But for now, Hezbollah is treading lightly to maintain some good will with other sects and religious communities — and Hasbayya residents are doing what they can to deter the group.

“We don’t want any strangers or anyone related to Hezbollah here,” said Ghassan Halabi, the deputy mayor of Hasbayya, told visiting New York Times journalists last month. “It took us years to build this town and it could all be destroyed within minutes. We can’t allow that to happen.”

Sprawled across the foothills of Mount Hermon, Hasbayya is only six miles from the Israeli border. Winding roads connect clusters of houses and thickets of olive and pine trees, as well as ancient ruins dating back to the Crusader period. The town is home to about 30,000 people, mostly Druse Lebanese — adherents to a 1,000-year-old religion — as well as Christians and some Sunni Muslims.

These days, Hasbayya is cloaked in the din of war raging around it: The booms of artillery shells, the buzz of drones and the screech of Israeli jets overhead. When airstrikes hit in the distance, plumes of smoke curl into the air along the green slopes of mountains.

When Hezbollah began launching rockets into Israel last year in support of Hamas, prompting months of tit-for-tat strikes, local leaders in Hasbayya and other nearby Christian and Sunni villages approached Hezbollah officials in the area with a request.

We asked them “not to launch rockets from inside the town,” said Wissam Sliqqa, a Druse sheikh and local leader in Hasbayya. “We wanted to preserve the safety of our residents and ensure they could remain in their homes” and not be forced to flee north, he explained.

Hezbollah leaders agreed. But when the war intensified and Israeli airstrikes began pummeling villages on the edge of Hasbayya, panic took hold.

Worried that Hezbollah fighters might fall back to Hasbayya, dozens of residents volunteered with the municipality police to work shifts on a new neighborhood watch. They created a WhatsApp group for people in nearby villages to flag anything suspicious. The mayor, Abu Nassar, imposed an 8 p.m. curfew, after which all residents must remain inside their homes. After midnight, no cars are allowed to enter or drive through Hasbayya.

Those efforts are trying to fill the void left by the Lebanese National Army, which has never been strong enough to defend the country against invaders. Local officials know that their ragtag efforts can do little to protect Hasbayya against Israeli ground troops or airstrikes. But they hope the scouts can prevent Hezbollah fighters from setting up positions within the town. They can also alert residents in time to flee if Israeli troops do move forward.

“We’re worried,” said Kanj Nawfal, a municipal police officer who oversees the volunteer guards. “We are trying to be careful but if something happens,” he added, his voice trailing off. He wrung his hands, searching for the right words.

“This war is bigger than us,” Mr. Nawfal explained.

The town’s fears are rooted in the wreckage of nearby villages, damaged as the wake of destruction in Israel’s fight against Hezbollah has widened. In recent weeks, hundreds of people fleeing nearby villages flooded into Hasbayya looking for refuge.

Mohammad Fares, 34, arrived in late September from Chebaa, a mostly Sunni town wedged between Hasbayya and the Israeli border. The town had mostly been insulated from the strikes until late September when, around 2:30 one morning, an Israeli airstrike crashed into his neighborhood and killed a family of nine, according to residents.

Hours later, another airstrike landed in the town. Mr. Fares and his neighbors clambered into cars — some carrying more than a dozen people — and sped toward Hasbayya.

“It was like nowhere is safe anymore,” Mr. Fares said.

Mr. Fares, who is Sunni, found refuge in Kfeir, a village in greater Hasbayya, in a high school that was hastily converted into a shelter. In the days that followed, other families fleeing Marjayoun, a Christian city to the east, flocked to the school too. But local officials closed the doors when Shiite Muslim families leaving villages that are known to have deep-seated support for Hezbollah arrived.

“Families came and we told them, respectfully, there is no more space in our shelters,” said Mr. Halabi, the deputy mayor.

Mr. Halabi’s misgivings reflect the evolving pattern of Israeli airstrikes that have moved from solely Shiite pockets of Lebanon to also include areas home to mostly Christian, Sunni Muslim and Druse Lebanese, which were once considered safe. While many shelters in other towns have offered refuge to people of all religious backgrounds, strikes on houses and apartments hosting displaced families have stirred fears in Hasbayya that Hezbollah fighters are blending in with refugees, prompting Israel to strike them.

The limits of efforts to keep the town safe were made real last month: An Israeli airstrike leveled a guesthouse in the town, killing three journalists from Lebanese news outlets either owned by or seen as sympathetic to Hezbollah. It was the first strike within the town limits since the war escalated — and stoked fears that it was no longer off-limits.

“We don’t have problems with anyone, we don’t have outgoing rockets, we just want stability,” said Nayef el Hassaniyeh, 59, as he stood on his rooftop on the southern edge of the town one recent afternoon.

From his perch overlooking the mountains, Mr. Hassaniyeh patiently scanned the escarpments across from him. Almost every night since the conflict escalated, the spine of the mountains in the distance light up with the flash of airstrikes — a real-time map of the war’s path.

Mr. Hassaniyeh and some of his neighbors fear the strikes in the Sunni and Christian towns in the distance foreshadow Hasbayya’s fate if the war drags on. If cities where Hezbollah does not have support could be hit, they wonder, what is to stop Israeli airstrikes from raining down on theirs as well?

“This war has been imposed on us. Did we choose it as Lebanese? No. They imposed it on us,” Mr. Hassaniyeh said, referring to Hezbollah. “We just want to protect ourselves. We just want peace.”

Iran’s supreme leader on Saturday threatened “a crushing response” to Israeli strikes on his country, as the Pentagon said it would deploy additional resources to the region in the coming months.

Tehran initially appeared to play down the damage caused by Israeli strikes inside Iran late last month, raising hopes that it might de-escalate the situation rather than pursue a new cycle of retaliation. But in recent days, Iranian officials have changed their tone.

Iran’s supreme leader, Ayatollah Ali Khamenei, has the authority as commander in chief to order strikes on Israel. In a statement posted online, he said on Saturday that Israel and the United States would “definitely receive a crushing response” for actions against Iran.

His remarks echoed two Iranian officials who this past week said that Iran would retaliate, with one telling state news media that a response would be “definite” and a second saying Iran would launch “a fierce, tooth-breaking” response.

After years of avoiding direct military clashes, Iran and Israel have been locked in an escalating monthslong cycle of retaliation that has drawn in their allies and proxies, bringing the region to the brink of an all-out war.

The Pentagon in late September extended the deployment of an aircraft carrier strike group in the Gulf of Oman to deter Iranian attacks and shoot down any ballistic missiles fired into Israel.

To maintain those kinds of capabilities in the region when that carrier, the U.S.S. Abraham Lincoln, returns to its home port, the Pentagon announced late Friday that a new deployment of ships and land-based warplanes would head to the region.

Maj. Gen. Pat Ryder, the Pentagon press secretary, said that Defense Secretary Lloyd J. Austin III had ordered the deployment of fighter aircraft, ballistic missile defense destroyers and B-52 long-range bombers to assist in the defense of Israel and other U.S. interests in the region.

“Secretary Austin continues to make clear that should Iran, its partners, or its proxies use this moment to target American personnel or interests in the region, the United States will take every measure necessary to defend our people,” General Ryder said in a statement.

The United States has already bolstered its military presence in the region as tensions rise. It sent an advanced missile defense system, called the Terminal High Altitude Area Defense system, or THAAD, and the 100 American troops needed to operate it, to Israel.

Their arrival less than two weeks ago was the first time that U.S. troops had been deployed to Israel for such a mission since the start of the war last October.

The Biden administration sent key envoys, including the C.I.A. director, to the Middle East this week in hopes of generating some momentum in talks to end Israel’s war against Hamas in Gaza and its spiraling conflict with Hezbollah in Lebanon. Both groups are Iranian proxies. But those efforts have floundered, and the fighting has continued unabated.

On Saturday, Lebanon’s health ministry said that one person had been killed and 15 others had been wounded by an Israeli airstrike in the Dahiya, a densely populated area south of Beirut where Hezbollah holds sway. The previous day, heavy Israeli strikes killed at least 52 people in the central part of the country, the Lebanese authorities said, and seven people in northern Israel were killed by Hezbollah rocket attacks.

The Israeli military said on Saturday that its forces had struck more than 120 sites in both Lebanon and Gaza since the day before, including an airstrike in the Lebanese city of Tyre that it claimed killed two Hezbollah commanders. It also said troops were conducting ground operations in northern, central and southern Gaza.

In central Israel early on Saturday, a rocket strike hit Tira, an Arab-majority town in central Israel, and injured several people. The Israeli military said that three rocket launches had been detected overnight from Lebanon, including at the region that includes Tira. Another 30 launches from Lebanon were detected on Saturday afternoon, the military said.

Magen David Adom, Israel’s emergency medical service, said 11 people were wounded in Tira, with most of the injuries minor to moderate. A photograph and a video posted by the emergency service showed the top floor of a building with its walls blown out.

Hezbollah started striking Israel in solidarity with Hamas, its ally in Gaza, after the Oct. 7 Hamas-led attacks last year prompted Israel to launch a war against the group in Gaza.

After nearly a year of cross-border attacks that primarily landed in the border region, Hezbollah in recent months has taken aim deeper inside Israel. The militant group launched missiles at the densely populated Tel Aviv area in September and October. Those were intercepted with no reported injuries or damages.

Victoria Kim, Rawan Sheikh Ahmad and John Ismay contributed reporting.