The crowd grew as it marched north, blocking streets. Later, in Union Square, a separate event organized by left-leaning Jewish groups was held to mourn the Palestinian, Israeli and Lebanese victims of the past year.

“I’m protesting one year of killing human beings who don’t deserve to die,” said Mir Ali, 67, of Staten Island, who was among the protesters in Lower Manhattan. Israel’s campaign in Gaza has killed more than 41,000 Palestinians, many of them children, according to local health officials.

Several of New York’s highest-ranking elected officials including Gov. Kathy Hochul and Mayor Eric Adams, appeared at another event in Central Park memorializing the victims of the attacks on Oct. 7, when officials say 1,200 people who were killed and roughly another 250 were taken hostage. During emotional remarks by the parents of 22-year-old Omer Neutra, who is being held by Hamas, the crowd of more than a thousand, many waving Israeli flags or draping them around their shoulders, broke into the rallying cry that has been repeated throughout the past year: “Bring them home.”

The protests across the city remained peaceful. By Monday afternoon, at least one person had been arrested as the protesters moved across Manhattan, according to police officials.

The day of remembrance and protest follows a year of demonstrations around the city. Many protesters have expressed outrage over U.S. funding and support for Israel’s actions in Gaza. Other events have focused on the return of the hostages. As the war has broadened in recent days, pro-Palestinian demonstrations have also denounced Israel’s attacks on Lebanon, where at least 2,000 people have been killed and hundreds of thousands displaced since Israel invaded to fight Hezbollah.

The events over the past year, particularly on the city’s college campuses, have sometimes turned volatile and have included clashes with the police.

Feelings about the conflict have been raw in New York, which is home to the largest Jewish community outside Israel — nearly 1 million in the city — and also has about 6,825 residents who identify as Palestinian, according to the U.S. census. Since last October, the city has seen rising instances of antisemitic and anti-Muslim violence and harassment.

At Columbia University, where student encampments opposing the conflict earlier this year inspired similar protests at campuses nationwide, both pro-Palestinian and pro-Israel demonstrators gathered on Monday to speak about the impact of the war.

Addressing a group of people gathered outside Columbia’s gates holding Israeli flags and posters with photos of hostages, Shai Davidai, an assistant professor at Columbia’s business school, said, “This day is about us,” adding: “We are still here, and we are not going anywhere.”

When the pro-Palestinian demonstration in Lower Manhattan reached Washington Square Park, it merged with a gathering of hundreds of student protesters. The group marched to Union Square, where it paused again for prayers before continuing north.

Ritty Lukose, 55, a professor at nearby New York University, said she viewed the day as one of mourning, including for those in Gaza who have been killed or whose lives have been upended.

“This is not to erase the suffering of the people” who were victims of Hamas’s attack, she said. “But this is to put it in context.”

As the new school year began and Oct. 7 approached, some universities that had seen protests earlier in the year updated their policies around student action. Mayor Adams said that security would be enhanced around synagogues for the High Holy Days — the anniversary falls between Rosh Hashana, the Jewish New Year, and Yom Kippur, the Day of Atonement — and that the police would be prepared to handle demonstrations.

“To those who plan to use this day to peacefully protest, that is your right,” Mr. Adams said on social media on Monday morning. “As you do so, remember to follow the law and I ask you to please hold a place in your hearts for those who lost everything a year ago today.”

Ahead of the evening memorial event at Central Park’s SummerStage, security had been ramped up, with armed officers guarding entrances and either side of the stage.

A line of elected officials — Ms. Hochul, Senators Charles Schumer and Kirsten Gillibrand, the House minority leader, Hakeem Jeffries, Attorney General Letitia James and Comptroller Tom DiNapoli — carried candles to center stage and stood silently, heads bowed and hands clasped, as a cantor sang a prayer. Behind them, a giant screen flashed photographs of those killed on Oct. 7 and those still in captivity, along with video clips of Israeli soldiers, tanks and warplanes. After more prayers and musical performances, including by the singer-songwriter Regina Spektor, the event concluded with the playing of the U.S. and Israeli national anthems.

Around 6 p.m., the pro-Palestinian demonstration changed directions and gathered in Madison Square Park. The call to prayer sounded, and the crowd fell mostly quiet as drones and helicopters hovered overhead. After the prayers, the crowd chanted “Gaza,” accompanied by drums and horns. Around 7:30 p.m., the demonstrators began to disperse.

Separately in Union Square, hundreds of people sang at a memorial organized by Jews for Racial and Economic Justice and several other left-leaning Jewish groups. As speakers called for an arms embargo, an immediate cease-fire and a deal to return the hostages, the crowd — some wearing kaffiyehs or kipas, some holding signs with slogans like “Palestinian and Jewish Safety Are Intertwined” and “Not Another Bomb” — was solemn.

As the names of Palestinian, Israeli and Lebanese civilians who have been killed in the past year were read aloud, quiet sobs were the only sounds. Attendees stood to light yahrzeit memorial candles and leave small stones at the feet of the speakers.

“It’s hard to be here knowing that despite the efforts of so many people, it hasn’t stopped,” said Zoe Goldblum, a 28-year-old Park Slope resident who works at a Jewish nonprofit.

“But we’re still here, because there are still people living in Gaza and in Israel and in Lebanon who deserve our voices and who need us to be out here, showing that we hear them,” she continued. “They deserve to live.”

Lucy Tompkins, Connor Michael Greene, Olivia Bensimon, Romaissaa Benzizoune and Nate Schweber contributed reporting.

Student groups sympathetic to either the Israelis and the Palestinians used the anniversary to host speakers, teach-ins and protests at campuses across the country, from Boston to Los Angeles. In advance of the day, administrators fretted over how to balance safety with free expression.

At least at Maryland, the university had not struck the right balance, according to a U.S. district judge, Peter J. Messitte.

The school’s administrators had first said they would allow the event, which was organized by the university’s chapter of Students for Justice in Palestine. They reversed course last month, citing security concerns, and said they would prohibit all expressive activity by student groups on Oct. 7. In court filings, lawyers for the university said that it had received “credible threats of violence” connected to the pro-Palestinian event.

Students for Justice in Palestine, aided by two other organizations, Palestine Legal and the Council on American-Islamic Relations, sued the university, arguing that it had violated the student group’s First Amendment rights. They portrayed the school as having censored the event after pro-Israel individuals and groups complained and having justified the decision by citing vague safety concerns.

The university had, before prohibiting the event, considered moving all classes and events online for the day. “The university’s goal has not been to silence S.J.P., but to protect its members and all community members from a credible risk of violence,” it wrote in court documents.

But the atmosphere on campus on Monday was relatively calm as the pro-Palestinian demonstrators set up a display — and pro-Israeli demonstrators set up another nearby.

The weather was warm and sunny, and by midday, a small crowd gathered on a campus lawn with a fountain. Pro-Palestinian activists, surrounded by TV crews, handed out “For Gaza We Rise” fliers to students hurrying between classes. Some flew white kites in the early-fall breeze. Several students spread blankets and pulled picnics from coolers.

Daniela Colombi, 20, a member of Students for Justice in Palestine who is studying astronomy and physics, said the group expected additional people because of attention brought by the lawsuit.

“Oct. 7 is a flashpoint day,” she said, adding, “We wanted to get as much attention as possible.”

By the evening, the vigil that the university had sought to prevent had drawn several hundred people. Someone read a list of Palestinian children killed in Gaza. Another recited a poem by a Palestinian writer who also died. The crowd listened silently.

Some Jewish student groups had celebrated the university’s earlier decision to curb the pro-Palestinian event. The Jewish Student Union on campus said in a statement that the anniversary should be “a day of mourning for the Jewish and Israeli community” and that the university’s decision “ensures that our physical and psychological safety is protected on this day of grief.”

The pro-Israel students’ display included more than 100 folding chairs as a tribute to the hostages abducted from Israel on Oct. 7. Elle Schanzer, 20, a sophomore from New York, handed out yellow hostage pins to students and faculty. Several chatted quietly or stood silently in front of photos of the hostages.

“It’s a space where you can be one with your thoughts,” Ms. Schanzer said.

She said that she saw an opportunity to hold the event when the judge’s ruling forced the school to permit the Palestinian demonstration. “I think everyone has the right to speech,” she said. “I don’t know if I agree with the way they went about it,” she added, but turning toward the posters, said “it gave us the opportunity to do this — which is amazing.”

Lawyers for the university had argued that Students for Justice in Palestine had been approved every time it applied to host an event over the last year — garnering a total of more than 70 OKs — despite vociferous opposition. But they said that the security concerns around the Oct. 7 events were “of a different nature and degree” than any event in the previous year.

They cited an example, saying that on Aug. 30, two days before the university’s president, Darryl J. Pines, announced that the Oct. 7 event would not be allowed, a university lawyer received a call from someone who said she was “locked and loaded” and would bring a gun to campus for self-defense.

In granting the pro-Palestinian group’s request for a preliminary injunction last week, thereby effectively allowing the event to go forward, Judge Messitte wrote, “This is a matter of law, not of wounded feelings.”

The university had other options besides barring the event, he wrote, including employing extra security personnel, installing temporary metal detectors and checking for student identification. In the end, the university ended up enhancing security for the vigil.

The year had been “incredibly hard” as Jewish students tried to navigate the crisis in the Middle East even as their own community was divided over how to respond, said Uri Cohen, executive director of Yale’s Slifka Center, which is affiliated with the university’s Hillel chapter, in an emailed statement to supporters.

Amid rising antisemitism, “Jews everywhere were reminded that we must look out for ourselves,” he wrote. At the same time, “tension between Jews forced us to get clear about who we are and what values we hold.”

Harvard Hillel was holding a public memorial on the steps of the university’s Widener Library. The Hillel rabbi and executive director, Jason Rubenstein, said he saw the public nature of the memorial as being in the Jewish tradition of mourning those close to you yet also supporting others in their grief during their time of loss.

“We hope our neighbors will attend and support us and comfort us, and at other times, other communities on campus will grieve their losses, and it’s our responsibility as their neighbors to show up and attend to them,” he said in an interview.

“There’s a real weightiness, a lot like 9/11,” Rabbi Rubenstein added. “It feels like we have to do this work together.”

At the University of Maryland, Hillel was offering “emotional support” and “stress relief” for any students unnerved by the protests going on, said Rabbi Ari Israel, executive director of the campus chapter.

At the University of Pennsylvania, Hillel called for a day of mourning for the lives lost on Oct. 7 and throughout the war. Events included a five-hour reading of the names of the 1,200 killed in the initial attack and the screening of a film, “Screams Before Silence,” depicting the events at the Nova music festival, where nearly 400 people were killed.

Dan Grushkevich, a second-year law student at the University of California, Berkeley, went to several events at the Berkeley Hillel commemoration on Monday.

“I was born in Israel and my family immigrated to the U.S., and so this was a hard day for me,” he said, “and I felt like I needed to channel my energy into something more positive than just sitting and being sad on my own and scrolling on the internet.”

One event was about fasting and memory in the Jewish tradition. Another event was about seven lessons of the last year. He was most struck by one about being an ally. For many American Jews, he said, “you don’t know who to trust and who holds beliefs or opinions that lack in empathy with the way you feel and the difficulties that you’re having.”

At the Harvard vigil, people held candles and listened to Harvard students sing “October Rain.” Peter Levin, a senior studying psychology at Harvard, said he felt the gathering was “a beacon of hope for Jewish people around campus.”

In some ways, Rabbi Rubenstein got his wish, Mr. Levin added. “There were people there who weren’t Jewish, people who I knew, people to support, which was impactful,” he said.

The right-wing Israeli government, which is led by Prime Minister Benjamin Netanyahu, held an official ceremony in Ofakim, a working-class town on the Gaza border that trends conservative and religious, and a recording of it was presented to television viewers. Members of the left-leaning kibbutzim — communal villages along the Gaza border — joined an alternative vigil in liberal Tel Aviv, which was broadcast live.

Many of the families and communities devastated in the Hamas attacks, particularly the kibbutzim, boycotted the official ceremony, saying that Mr. Netanyahu had yet to take personal responsibility for his failure to prevent the disaster. They also accuse him of not doing enough to bring home the remaining 100 hostages still in Gaza, more than 30 of whom are believed to be dead.

Hundreds gathered in Tel Aviv instead for the vigil, which they hoped would better express their bitter disappointment in the government’s failure to protect them last Oct. 7, when many had spent hours in hiding as Palestinian militants overran their villages, killing residents and workers and taking others hostage.

“It was a day without an army, without a state — a day where all we had was ourselves, the citizens,” Jonathan Shimriz, one of the vigil’s organizers, said in his closing speech. “This is what abandonment looks like.”

Tens of thousands of Israelis had snapped up tickets to attend the vigil. But with violence spiraling with Hezbollah and the possibility of parallel attacks from its backer, Iran, the police ultimately restricted attendance to a handful of people, mostly the families of hostages and bereaved Israelis.

Mr. Shimriz’s brother, Alon, was abducted to Gaza from the border village of Kfar Azza on Oct. 7. He was accidentally shot dead alongside two other hostages by Israeli soldiers as they emerged from a building in Gaza, waving a white flag. The military said the troops had mistaken them for Palestinian militants.

In his speech at the vigil, Mr. Shimriz excoriated the Israeli government, which he said had failed to credibly investigate “the colossal failure” that led to the Oct. 7 attacks and his brother’s abduction. “We ask the questions ourselves without getting any answers,” he said.

The official ceremony — organized by Miri Regev, a member of Mr. Netanyahu’s Likud party — offered fewer calls for soul-searching in the wake of the disaster. The event featured remarks from survivors, wounded soldiers, relatives of those killed, lyrical psalms and a video address by Mr. Netanyahu, who vowed to press on with the war.

“As long as the enemy threatens our existence and our country’s peace, we will keep fighting. As long as our hostages are in Gaza, we will keep fighting,” said Mr. Netanyahu. “We will keep fighting — and together we will win,” he added.

The events since Mr. Biden’s remarks have demonstrated the limits of his influence in the region. Even as the United States has continued to arm Israel, the administration has been repeatedly thwarted in reining in Mr. Netanyahu, who has sidestepped or dismissed entreaties from the White House to de-escalate the conflict and leave room for a postwar creation of a Palestinian state. And with Israel now poised to carry out retaliatory strikes against Iran, the wider war that Mr. Biden sought to avert is at hand.

“The gap between what Biden hoped to achieve and what ultimately he was forced to encounter is as wide as the Grand Canyon,” said Aaron David Miller, a senior fellow at the Carnegie Endowment for International Peace.

In the 2020 campaign, Mr. Miller said, Mr. Biden promised voters that “America was going to be back, it was going to lead again” on the international stage. But the year since the Oct. 7 attacks in Israel “shows the limitations of American influence and power.”

On Monday, Mr. Biden marked the first anniversary of the Hamas-led attacks by lighting a yahrzeit candle in memory of the dead during a ceremony in the Blue Room at the White House. Rabbi Aaron Alexander of Adas Israel Congregation in Washington conducted a brief ceremony, praying for “the souls of the holy ones, men, women and children who were killed on October the seventh.”

In a telephone call with President Isaac Herzog of Israel on Monday, Mr. Biden promised to “never give up” efforts to bring home the remaining hostages being held by Hamas. He expressed what the White House said was “deep sadness” about the loss of life in Gaza, but vowed to remain steadfast in helping Israel defend itself.

Mr. Biden did not talk with Mr. Netanyahu on Monday, extending the silence between the two men that has existed since they spoke on Aug. 21, nearly seven weeks ago.

The tension between Mr. Biden and Mr. Netanyahu has been at the center of questions about the way his administration has handled the situation in Israel: How do you pressure an ally facing a threat to its existence? How far should you go if that ally ignores your advice? And, with just 29 days before the next presidential election, how do you explain the unrelenting violence both to voters who feel he has been too deferential to Israel and to those who think he has not done enough to support Israel?

Vice President Kamala Harris, who replaced Mr. Biden as the Democratic presidential nominee, is now facing the electoral consequences of those questions. In a statement Monday, she pledged that she will “never stop fighting for justice” for those killed by Hamas, but also saying she is “heartbroken over the scale of death and destruction in Gaza.”

Over the past year, the administration has made halting progress and some modest achievements — all of which fell far short of the goals Mr. Biden laid out nearly a year ago.

In his remarks in Tel Aviv that day, Mr. Biden pledged to secure the release of the people taken by Hamas, including some United States citizens, saying that “for me as the American president, there is no higher priority than the release and safe return of all these hostages.”

A year later, nearly 100 hostages still remain in captivity, including Americans, while some others have been killed. Hostages were released in a cease-fire deal in November, but at the end of August, Hersh Goldberg-Polin, an American who had been living in Israel, was among six hostages killed by Hamas.

Mr. Biden vowed a year ago to help ensure that civilians in Gaza received “food, water, medicine, shelter” amid Israeli fighting. Over the past year, Americans helped negotiate increased aid deliveries, but even those have fallen far short of what is needed, according to global health officials.

Mr. Biden’s message then included a blunt warning to Iran and others in the Middle East not to use the fighting in Gaza as an excuse to attack Israel. “My message to any state or any other hostile actor thinking about attacking Israel remains the same as it was a week ago,” he said. “Don’t. Don’t. Don’t.”

In the year since, those warnings have proved ineffective. Iran has twice launched missile attacks directly against Israel, including last week, and Mr. Netanyahu is now weighing options for retaliatory strikes. Hezbollah’s near-constant barrage of attacks from Lebanon over Israel’s northern border has triggered a vast Israeli military response over the past several weeks, including the killing of Hezbollah’s leader.

Mr. Biden urged Israel not to give in to rage as it considered how to react to the worst attack on the Jewish people since the Holocaust. He compared the decisions facing Israel to the ones that the United States had to make after the terrorist attacks of Sept. 11, 2001.

“We were enraged in the United States,” he told the Israeli people that day. “And while we sought justice and got justice, we also made mistakes.”

The decisions by Mr. Netanyahu and his cabinet mirrored those of the post-9/11 American politicians who felt that only war would ensure long-term security. At several points during the past year, Mr. Biden and his team have been unable to talk Israel down from escalation.

As the conflict with Hezbollah intensified, Mr. Biden succeeded in rallying almost a dozen nations to call for a cease-fire. But their proposal foundered almost immediately when Mr. Netanyahu approved the killing of Hezbollah’s leader, Hassan Nasrallah, just hours later.

Mr. Biden has only 105 days left in his term, and like many of his predecessors, he faces the prospect of leaving office frustrated by the cycles of conflict in the region. But on Monday he vowed to keep working toward the goals he articulated that day in Tel Aviv.

“We will not stop working to achieve a cease-fire deal in Gaza that brings the hostages home, allows for a surge in humanitarian aid to ease the suffering on the ground, assures Israel’s security and ends this war,” he said in an early morning statement.

“Israelis and Palestinians alike,” he wrote, “deserve to live in security, dignity, and peace.”

Isabel Kershner recalls visiting a Hamas hostage cell during an escorted visit to Gaza with the Israeli military.

We walked in single file, by flashlight, until we arrived at a stifling, tiled chamber with a dirty sink. That led to bare cells, each with a mattress, toilet and basic shower.

I tried to imagine being held captive there by gunmen, not knowing when, how or even if the ordeal might end. After two hours in the tunnels, we re-emerged into daylight, returned to the border and stepped back into a more familiar world.

Raja Abdulrahim writes about a video of a child’s grave in Gaza.

Access to Gaza is largely cut off, but the devastating last year of war there has been clearly visible in videos and images, many of them heartbreaking. Bloodied bodies being pulled from the rubble of Israeli airstrikes. Families fleeing their homes with the few belongings they can carry. Children sifting through garbage to find scraps to eat.

The video of Kareem’s grave, by comparison, is almost sterile. There are no sounds and no blood. Just a tree and a small mound of dirt, the final resting place of one of the many young victims of the war in Gaza.

Adam Rasgon writes about a young Gazan doctor who fled to Egypt.

He told me about his frustrations with not being able to work in Egypt and his guilt for leaving behind the emergency rooms and his family in Gaza. His story felt to me like those of so many other civilians caught in the crossfire in Gaza, struggling to survive and find a path forward.

“We must work to ensure nothing like the horrors of Oct. 7 can ever happen again,” she said. “And on this solemn day, I will restate my pledge to always ensure that Israel has what it needs to defend itself, and that I will always work to ensure the safety and security of the Jewish people here and around the world.”

While Ms. Harris did not call for a cease-fire in Gaza during her prepared remarks — as she has in the past — she acknowledged the more than 41,000 Palestinians who have died, according to local health officials, in Israel’s campaign to eliminate Hamas.

“We must work to relieve the immense suffering of innocent Palestinians in Gaza who have experienced so much pain and loss over the year,” she said.

During the vice president’s remarks, protesters could be heard chanting in the background.

The brutality of the Oct. 7 attacks and the mass death and grave humanitarian crisis in Gaza caused by Israel’s response have complicated Democratic efforts to win support from Jewish, Muslim and Arab American voters, groups that have reliably backed the party in past elections.

Republicans have tried to use Israel as a wedge issue with Jewish voters, although former President Donald J. Trump has sometimes seemed to hamstring those attempts by claiming that American Jews who support Democrats hate their religion or are disloyal. And many Muslim and Arab Americans, particularly in the battleground state of Michigan, say they will not vote for Ms. Harris because she has not spoken out more strongly against the United States’ military and financial aid to Israel.

On Monday, all four candidates on the Democratic and Republican tickets publicly honored the Oct. 7 anniversary, as did President Biden, reflecting how deeply felt the attacks have been in the United States.

After Ms. Harris and Mr. Emhoff shoveled dirt over the base of the newly planted pomegranate tree, the vice president said in response to a reporter’s question that negotiating a cease-fire in Gaza was “one of the highest priorities of this administration.”

“We are not going to give up,” Ms. Harris said. “We are doing everything we can possibly do to get a cease-fire and hostage deal done. It’s one of the most important ways we will be able to end this war and bring any type of stability to the region.”

Earlier in the day, Mr. Biden participated in a candle-lighting ceremony at the White House to remember those killed on Oct. 7. He lit a yahrzeit candle and briefly crossed himself without making remarks.

Also on Monday, Mr. Trump observed the anniversary of the attack by visiting the grave in New York City of Rabbi Menachem M. Schneerson, an influential leader of the Lubavitcher movement, a Hasidic group, who died in 1994. Mr. Trump is also scheduled to travel to Florida for an event on Monday evening with Jewish community leaders at his resort in Doral.

His running mate, Senator JD Vance of Ohio, attended a memorial in the shadow of the Washington Monument in the U.S. capital, and used the platform to criticize Mr. Biden and Ms. Harris for their policies in the Middle East, asserting that they “haven’t done a thing” to bring home the hostages still held by Hamas. He also denounced pro-Palestinian protesters as “pro-Hamas,” saying that their calls for a cease-fire were equivalent to calling “for a unilateral surrender.”

Ms. Harris’s running mate, Gov. Tim Walz of Minnesota, who was traveling in California, marked the anniversary by paying his respects at the Nova Exhibition, an installation that moved from Tel Aviv to New York to Culver City and is dedicated to the music festival where more than 380 people were killed in the Hamas-led assault.

Reporting was contributed by Michael Gold, Chris Cameron and Katie Glueck.

One of the people I’ve spoken to the most is Omar al-Najjar, 24, a doctor from southern Gaza, who was dealt the difficult hand of caring both for patients in emergency rooms — most with critical injuries from Israeli attacks — and his displaced parents. (Last October, the journalist David D. Kirkpatrick and I chronicled his harrowing experience at a hospital in southern Gaza for The New Yorker.)

Israel has prevented foreign reporters from visiting Gaza during the war except for occasional, highly controlled embeds with soldiers. The dozens of Gazans I’ve stayed in touch with, some on a daily basis, have offered me glimpses into their lives: the aftermath of Israeli bombardments, the miserable conditions in displacement camps, Hamas’s violence against Palestinians.

In my conversations with Mr. Najjar, a theme that comes up often is survival.

He has lost nearly 100 friends, relatives, and colleagues in the war, he said. His childhood neighborhood was leveled as a part of an Israeli effort to create a buffer zone between Israel and Gaza. His family has relocated some 15 times in search of safety, sometimes fleeing with bombs falling behind them.

In December, he shared an Instagram post that he told me had been inspired by his reading of “Hiroshima,” a 1946 essay in The New Yorker by John Hersey about six people who survived the atomic bomb.

“For days, John Hershey’s words have stayed with me,” he wrote. “He mentioned their profound question — why were they chosen to survive while many didn’t?” he added. “That will be my profound question, (if I make it).”

Mr. Najjar was able to escape Gaza on May 5, a day before the Rafah border crossing with Egypt was closed after Israel seized control of it. He never wanted to leave the territory, but decided it was best after having seen the scale of destruction in the city of Khan Younis.

The plan was for him to leave first, and he hoped to arrange for his parents and siblings to join him. He made it to Cairo. But the Rafah crossing remains closed, and his family is still in Gaza, in a town east of Khan Younis.

I last spoke to Mr. Najjar on Wednesday. He told me about his frustrations with not being able to work in Egypt and his guilt for leaving behind the emergency rooms and his family in Gaza. His story felt to me like those of so many other civilians caught in the crossfire in Gaza, struggling to survive and find a path forward.

“Perhaps I’m being punished for betraying Gaza,” he said. “I just hope this nightmare comes to an end soon.”

Israel has been escalating its military raids in the West Bank in parallel with its offensive against Hamas in Gaza, describing it as an effort to root out militants who have increased attacks against Israelis. The raids began before the Hamas-led attacks last Oct. 7 in response to a burgeoning generation of fighters in northern West Bank towns like Jenin and Tulkarm — some of them tied to Hamas, but many of them younger Palestinians who do not feel beholden to the insurgent groups of previous generations that they say have failed them.

Since last Oct. 7, Israeli raids have intensified not only in their frequency but also in the scale of the wreckage they have created. Residents have called the Israeli military operations the most destructive they had ever seen, and videos taken during and after raids in Jenin and Tulkarm that were analyzed by The New York Times support their accounts of the damage.

“What’s happening is totally unprecedented, that is absolutely clear,” said Shawan Jabarin, the director of Al-Haq, a Palestinian rights group based in the West Bank.

The raids have been accompanied by rising violence by Israeli settlers and land seizures by Israel’s far-right government.

For years, violent factions within the Israeli settler movement, protected and sometimes abetted by the Israeli government, have grown into a grave threat to Palestinians. Since January alone, Israel has seized roughly nine square miles of the West Bank, by far the most in any calendar year, according to Peace Now, an Israeli group that monitors settler activity.

Mr. Jabarin and others see this as part of a coordinated effort to make life intolerable for Palestinians in the West Bank.

“This is not just a security operation — it is a political operation. And I expect it to keep expanding,” he said. The message to West Bank Palestinians, he added, is, “Gaza is coming to you.”

During a 10-day incursion into Jenin that began in late August, Israeli forces cut the city’s main water line for the 18th time since last Oct. 7, municipal authorities said. In Tulkarm, Muhanad Matar, a municipal official, said that workers had repeatedly rushed to repair a street or pipe damaged by raids — only to awaken the next day to a new military operation ripping it up again.

“The problem with trying to calculate the costs is that it doesn’t stop,” he said. “It’s an unending string of raids.”

In response to questions from The Times about destruction in the West Bank, Israel’s military said it “undertakes all feasible precautions to avoid damaging essential infrastructure.” But it acknowledged that “operations in the area have caused unavoidable harm to certain civilian structures.”

Some residents argue the level of destruction is an attempt to punish the entire population.

“They think they are teaching people a lesson,” said Rami Kamayel, who owns a store selling office supplies and toys in Jenin. He said his shop has been battered so many times this year by bulldozers and gunfights between Israeli forces and Palestinian militants that he has stopped replacing windows and signs.

Perhaps the heaviest impact has been on medical care. Red Crescent workers say their ambulances have been blocked by military vehicles and shot at, and that humiliating inspections and delays at Israeli checkpoints have left patients, including women in labor, waiting for hours to get to medical facilities, putting them at risk of bleeding out.

Israel’s military said that it “does not intend to harm medical personnel,” but that soldiers needed to conduct inspections because militants have exploited ambulances and medical centers to carry out attacks. Palestinian medical officials flatly deny the allegations.

Mohammed al-Saadi, director of the Red Crescent in Jenin, said that the international community had failed to hold Israeli forces to account for mistreatment of medical workers.

“These rights are clearly only for a certain part of society, one that discriminates against other parts of humanity,” he said. Now in the West Bank, he went on, “No one believes in human rights.”

Outside the university gates, about 100 members of the Jewish community gathered holding Israeli flags and posters showing the faces of people kidnapped by Hamas. Inside, on the steps of Low Library, at the center of campus, pro-Israel students made speeches about people who died at the Nova Music Festival last year.

Near them on the same steps, students who had walked out of class in support of Palestinians chanted, “Free, free Palestine,” and held flags and posters that read “Free Gaza, Free Speech” and “Join us Alumni.”

Columbia University and its affiliate, Barnard College, have sought to contain protests related to the Mideast conflict with new security measures, including locking campus gates and requiring students, faculty and staff to show IDs to enter. So far this school year, the atmosphere has been calmer, but many students and faculty say tensions are palpable.

Starting last week, Columbia University Apartheid Divest, a pro-Palestinian group, has been holding a vigil on the steps of Low Library. Unlike some past protests on and off campus, which have been marked by chanting and marching, the vigil has been somber. A few dozen students have often been gathered, sitting in silence, while others recite the names of those killed in Gaza.

At the foot of the campus’s Alma Mater statue last week, protesters set up a memorial featuring pictures of those who have died, along with Palestinian flags and a memorial garden laid out in the grass, but the college removed it and set up barricades. University security officers now stand watch nearby.

Joshua Shain, a biochemistry major and member of Students Support Israel, came to the pro-Palestinian vigil on Friday. He sat a distance away and held an Israeli flag, which he said was meant to raise awareness.

Mr. Shain said he had felt unsafe at times on campus in the past year. He recalled seeing a swastika in a campus bathroom and said that hearing people chant “Globalize the Intifada” had made him feel uncomfortable. But he said that this year felt “a lot less bad.”

A group of journalism students held their own tribute for the Palestinian and Lebanese journalists killed while covering the war in Gaza and the spillover conflict in Lebanon. As the students read each journalist’s name, the students laid a flower on the steps.

Earlier in the day, pro-Israel students had set up their own display, including a memorial for those who died at the Nova Music Festival in Re’im, Israel, on Oct. 7.

Eliana Goldin, who is a leader of Aryeh, a pro-Israel campus group, said the memorial was intended to help people “understand where we’re coming from and what the Jewish experience and the Israeli experience is like.”

After two hours on the library steps, around 200 pro-Palestinian students marched away, through the campus gates and onto city streets, shouting, “Free, free Palestine,” and “The people united will never be defeated.” They blocked intersections and placed stickers on street signs and police cars that read, “I said I loved you and I wanted genocide to stop.”

Several pro-Israel students remained on campus playing music in front of their memorial, but their speeches ceased.

Connor Michael Greene contributed reporting.

Instead, the documents challenge the court’s jurisdiction, arguing that Mr. Khan failed to provide sufficient notice of the scope of his inquiry or to give Israel time to show that it is capable of independently investigating the same matters. Under the treaty setting up the International Criminal Court, which Israel is not a party to, a case could be inadmissible in the court if it is already being or will be investigated by a state with jurisdiction over it.

That means if Israel has the ability to conduct its own investigation into the actions underlying the accusations against Mr. Netanyahu and Mr. Gallant, the International Criminal Court in theory could give precedence to the country’s judicial system, allowing it the opportunity to address the claims.

In this case, Israel has argued that Mr. Khan did not provide enough information about what he was investigating, nor did he give Israel the chance to show it would inquire into the allegations itself.

“Despite having been forced into a bloody conflict that it did not want, Israel remains a democracy endowed with an independent judiciary and deeply committed to the rule of law,” the Israeli filing argued, adding that Israel “has the appropriate mechanisms” to ensure accountability for any alleged crimes.

In May, Mr. Khan sought arrest warrants for Mr. Netanyahu and Mr. Gallant, and Israel is hoping to thwart or delay the issuance of the warrants. Mr. Khan also sought warrants for three Hamas leaders who were responsible for the Oct. 7 Hamas-led attacks that set off the war in Gaza — Yahya Sinwar, Ismail Haniyeh and Muhammad Deif. Of these three, only Mr. Sinwar is believed to still be alive.

Among other technical arguments rejecting the international court’s jurisdiction, Israel is now asking the I.C.C. to delay the request for arrest warrants for two of its top leaders until Mr. Khan provides more details about the scope of his investigation. And it wants the chance to show the court that it will address the accusations internally.

“Israel has primary jurisdiction and is best placed to investigate allegations of the sort raised by the Prosecutor, given the access required to relevant evidence, information and persons,” the Israeli submission argued.

The I.C.C. does have jurisdiction to proceed when a state is unable or unwilling to investigate accusations, or if the state inquiry is conducted in bad faith to protect the accused. And each situation is assessed on a case-by-case basis, so an Israeli inquiry wouldn’t necessarily preclude an I.C.C. prosecution going forward even if the court decides to grant Israel’s initial requests.

Nicknamed the “Merchant of Death” by U.S. officials, Mr. Bout was released by the Biden administration in December 2022 after serving less than half of his 25-year sentence in U.S. federal prison in connection to his work as an arms trader. The United States swapped him in the prisoner exchange that freed the W.N.B.A. star Brittney Griner from a Russian prison, where she had been held for 10 months after being arrested at a Moscow airport with 0.7 grams of cannabis oil.

Freeing Mr. Bout was long a priority for President Vladimir V. Putin of Russia. Western intelligence agencies do not have direct knowledge that the Russian leader told Mr. Bout to re-enter the arms trade, but officials said Mr. Bout would not have restarted his work without the implicit approval of the Kremlin. Had an arms deal with the Houthis been against Russia’s interests, they said, the Kremlin would have reined him in.

The Russians have been pursuing several weapons agreements with the Houthis, and Mr. Bout’s negotiations are not the only ones underway. Mr. Bout’s initial deal, reported earlier in The Wall Street Journal, was a potential agreement to transfer small arms to the Houthis. Western officials believe that other Russian officials and arms dealers are involved in potential agreements to send missiles to the Houthis from Russia.

More advanced and precise weaponry in the hands of the Houthis would allow them to target Israel more effectively and strike at ships in the Red Sea.

No arms or missiles had yet been transferred, Western officials said, but Mr. Bout is still coordinating his deal with the Houthis.

The officials believe the Kremlin is proceeding slowly and sending a message to the West with its negotiations with the Houthis. If Britain, France or the United States approves long-range missile strikes into Russia, Western officials said, the Kremlin is likely to complete the deal with the Houthis as part of an escalation strategy that seeks to apply pressure on the West without moving Russia closer to a direct war with the United States.

Mr. Bout has always denied accusations that he smuggles arms. He and the Kremlin both dismissed reports about the deal with the Houthis.

Dmitri S. Peskov, the Kremlin spokesman said in a call with reporters on Monday morning that the reports were an example of “fake or informational attacks on our elected representatives.”

In an interview on Monday with RBC, a Russian economic publication, Mr. Bout called the Wall Street Journal article a hoax but praised the Houthis, saying they had achieved results despite “insufficient resources.”

“They have, at least over the past year, shot down more than 10 American reconnaissance drones, and so all merchant ships that belong to the Americans or the Israelis have great difficulties passing through the Red Sea,” he said.

But Western officials believe Mr. Bout and the larger negotiations with the Houthis are part of a carefully calibrated effort to be ready to escalate tensions if the United States and its allies provide more support to Ukraine.

In addition to a stepped-up sabotage campaign in Europe, Russia is considering a broad campaign to assist groups like the Houthis and others challenging the United States and its allies if Washington removes restrictions on the use of American-made arms, Western officials said.

A recent U.S. intelligence report said Mr. Putin was likely to retaliate with greater force if the Biden administration allowed Ukraine to fire Western-made weapons deep into Russia.

The assessment described many possible Russian responses to a decision to allow long-range strikes using U.S.- and European-supplied missiles, such as increased acts of arson and sabotage targeting facilities in Europe and potentially attacks on U.S. and European military bases.

Mr. Bout, 57, was arrested in a U.S.-led sting operation in Thailand in 2008. He returned to Russia in December 2022 after the prisoner swap. Four days after returning, he joined the Kremlin-aligned, far-right Liberal Democratic Party. In July 2023, he won a seat in the Legislative Assembly of Ulyanovsk, a territory of 1.3 million people about 450 miles east of Moscow.

In an interview with The Times last year, Mr. Bout said that he needed time to learn to use a smartphone and that he was someone who had “very little of his business left, very little of my own life” and “nothing much left of any old contacts.” He acknowledged opening a business consulting company but dismissed the possibility of returning to his old line of work — one he insisted against all evidence had been “totally focused on logistics, different than the sales of weapons.”

On Monday, he told RBC he was working on a script for a feature film about himself.

“We are preparing our response to Hollywood,” he said, “and today’s clickbait is another good plot for one of the episodes in the series that is currently being prepared.”

“As we mark one year since Hamas’s brutal terrorist attack, Treasury will continue relentlessly degrading the ability of Hamas and other destabilizing Iranian proxies to finance their operations and carry out additional violent acts,” Janet L. Yellen, the Treasury secretary, said in a statement.

The United States estimates that Hamas has been raising as much as $10 million per month in donations from front charities. Europe is a major source of its fund-raising efforts.

The charity facing sanctions is called the Charity Association of Solidarity with the Palestinian People, which was founded by the Italy-based Hamas member Mohammad Hannoun.

The Treasury Department is also imposing sanctions on Al-Intaj Bank, a Hamas-run financial institution that the United States says is used to circumvent international sanctions.

Additionally, the United States is blacklisting Hamid Abdullah Hussein al Ahmar, a Yemeni national who lives in Turkey and who has helped to oversee Hamas’s $500 million investment portfolio. He chairs a “sham” Lebanese charity, Al-Quds International Foundation, according to the Treasury, which is also imposing sanctions on nine of his businesses.

“The Treasury Department will use all available tools at our disposal to hold Hamas and its enablers accountable, including those who seek to exploit the situation to secure additional sources of revenue,” Ms. Yellen said.

Israel’s ferocious air and ground war in Gaza has largely crippled or destroyed Hamas’s main military units, but the group remains capable of directing rockets toward Israel, which sometimes penetrate the country’s aerial defenses.

On Monday, four projectiles fired from Gaza fell in open areas in central Israel, and one was intercepted, according to the state broadcaster, Kan, which also said that one woman was slightly injured and that Ben Gurion Airport stopped flights for a time.

Israel’s military said its fighter jets struck the rocket launcher used to fire at Israel from the Khan Younis area, a city in southern Gaza that Israeli forces invaded in December in an attempt to crush Hamas, and then returned to months later to try to crack down on a Hamas resurgence.

During the strike in Khan Younis, “secondary explosions were identified, indicating the presence of weapons,” the Israeli military said in a statement. There was no independent confirmation of the claim.

A New York Times correspondent in Bani Suhaila, a town just east of Khan Younis, said an airstrike hit the area about 300 yards from where he was standing. Families fled on foot carrying their belongings after the strike, he said.

The military also said that it had struck a launcher in northern Gaza from which projectiles were fired toward Israel. The military did not say whether the projectiles landed in Israel, and Hamas did not comment on that claim.

Israeli forces first invaded northern Gaza last October, after telling residents to evacuate, and on Monday they again told residents in large parts of the area to leave because of an impending military operation.

A year after the Hamas-led Oct. 7 attack, Israel is battling both Hamas and Hezbollah, two armed groups backed by Iran who oppose Israel’s right to exist. Last week Israel followed up on its assassination of Hezbollah’s leader, Hassan Nasrallah, by sending tanks and troops over the border into southern Lebanon.

Lebanon’s state-run news agency on Monday reported intense Israeli airstrikes in southwestern Lebanon, where the Israeli military issued new evacuation warnings for over two dozen towns and villages.

The Israeli military said it was hitting Hezbollah targets. One hit Dahiya, the densely packed cluster of neighborhoods adjoining Beirut, where acrid smoke has been thick after waves of bombardment in recent days.

Lebanon’s health ministry said an Israeli strike on a fire station in Baraachit, in southern Lebanon, overnight killed at least 10 firefighters who were preparing to go on duty.

Israeli airstrikes have battered the country over the past couple of weeks, killing more than 1,000 people, according to a toll provided by the Lebanese health ministry. Its figures do not distinguish between civilians and combatants. Israel’s military also said on Monday that two of its soldiers had died in Lebanon over the past day.

In all, more than 2,000 people have been killed in Lebanon since the war began last October and nearly 10,000 others have been wounded, Lebanon’s health ministry said. Most casualties have occurred over the last three weeks, when Israel ramped up its offensive against Hezbollah. Israeli strikes killed 22 people and wounded more than 100 on Sunday alone, the ministry said.

Lebanon’s health ministry, Firass Abiad, has previously said that the number of dead and injured is likely an undercount, since it is only based on casualties reported by hospitals.

Hezbollah has for more than a year fired missiles and drones across the border and has continued those launches in the face of the Israeli onslaught.

Last month, Israel staged two waves of attacks in Lebanon via wireless electronic devices used by members of Hezbollah. Dozens of people were killed and hundreds were injured when the devices exploded, but many of those harmed were not part of the militia group. The Emirates statement did not mention the explosions.

Days after the incidents, Lebanon’s Civil Aviation Authority barred travelers from carrying such devices on flights leaving the international airport in Beirut, the Lebanese capital. In response, Qatar Airways said pagers and walkie-talkies would be prohibited, though only on flights between Doha and Beirut.

Emirates said in a statement on Monday that its flights to and from Lebanon will remain suspended until Oct. 15.