To his students, Ahmad al-Khatib was a deputy principal at an elementary school in Gaza run by the United Nations agency for Palestinian refugees. To Hamas’s military wing, documents say, he was something else entirely: an infantryman operating out of the southern Gaza city of Khan Younis.

The military wing, known as the Qassam Brigades, kept meticulous records of its fighters, tracking the weapons they were issued and regularly evaluating everything from their fitness to their loyalty.

Mr. al-Khatib, an employee of the U.N. agency since 2013, was among them: Secret internal Hamas documents shared with The New York Times by the Israeli government say that he held the rank of squad commander, was an expert in ground combat and had been given at least a dozen weapons, including a Kalashnikov and hand grenades.

The refugee agency, known as UNRWA, operated schools across Gaza before they were shuttered in the wake of Hamas’s Oct. 7 attack on Israel and the ensuing war. The agency, which employs roughly 13,000 people, including thousands in the schools, has a duty to maintain the neutrality of its facilities in the conflict zones in which it operates, including by keeping militants off its premises and payrolls.

But interviews and an analysis of the records shared with The Times by the Israeli military and foreign ministry indicate that Mr. al-Khatib was one of at least 24 people employed by UNRWA — in 24 different schools — who were members of Hamas or Islamic Jihad, another militant group. Before the war, the agency was responsible for a total of 288 schools, housed in 200 different building compounds, in Gaza.

A majority were top administrators at the schools — principals or deputy principals — and the rest were school counselors and teachers, the documents say. Almost all of the Hamas-linked educators, according to the records, were fighters in the Qassam Brigades.

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President Volodymyr Zelensky said on Sunday that 43,000 Ukrainian soldiers had been killed and 370,000 wounded since Russia’s full-scale invasion began nearly three years ago. It was the first time in months that he had disclosed military casualty figures, a highly sensitive topic in Ukraine, particularly as Kyiv’s forces lose more ground to Russian troops.

The Ukrainian leader’s tally could not be verified independently, and it differs sharply from estimates by U.S. officials and military analysts, who have put the number of dead much higher. U.S. officials said in August 2023 that close to 70,000 soldiers had been killed, a figure that has probably increased significantly since then.

Yuri Butusov, a Ukrainian journalist with close ties to the army, shared a similar figure last week, adding that 35,000 soldiers were also missing in action.

Mr. Zelensky also noted that about half of the wounded soldiers return to the battlefield after treatment. This suggests that Ukraine has suffered a total of about 230,000 irreplaceable losses, comprising those killed and those permanently incapacitated by injuries.

It was not immediately clear why Mr. Zelensky chose to release casualty figures now, but his statement came just a few hours after President-elect Donald J. Trump said that Ukraine had lost 400,000 soldiers, without specifying the number of dead or wounded. Mr. Trump, who also said that Russia’s casualties were close to 600,000 soldiers, said the high toll of the war underscored the need for an immediate cease-fire and the start of peace negotiations.

“I know Vladimir well,” Mr. Trump wrote Sunday on social media, referring to Russia’s president, Vladimir V. Putin. “This is his time to act. China can help. The World is waiting!” He urged Mr. Putin to begin negotiations and called on China, which has aligned itself with Russia on many issues, to join the process.

Ending the war was a major theme of a meeting between Mr. Trump and Mr. Zelensky in Paris on Saturday evening, their first in-person encounter since Mr. Trump won the U.S. presidential election last month. Mr. Trump’s promise to end the war quickly has raised fears in Kyiv that it could leave Russia in control of about 20 percent of Ukraine’s territory and strong enough to start another all-out offensive.

In an interview with NBC that aired Sunday, Mr. Trump said he would “probably” reduce aid to Ukraine when he returns to the White House next month.

Ukrainian officials in recent weeks have sought to forge ties with Mr. Trump and his future administration to try to shape their plans to wrap up the conflict in a way that best aligns with Kyiv’s interests.

Referring to his conversation with Mr. Trump in Paris, Mr. Zelensky said Sunday afternoon on social media, where he revealed the casualty figures, “I stated that we need a just and enduring peace — one that the Russians will not be able to destroy in a few years, as they have done repeatedly in the past.”

Anticipating that the new Trump administration may cut off aid to Ukraine to force it to the negotiating table, the Biden administration is trying to expedite the remaining military assistance earmarked for Ukraine. Late on Saturday, the Department of Defense unveiled a $1 billion package for Ukraine that will provide funds to buy ammunition for rocket systems, drones and spare parts for maintaining artillery equipment.

But American officials and military analysts have repeatedly said in recent weeks that additional weapons and ammunition are not what Ukraine needs most now. Rather, they say, it needs to do a better job of replacing its battlefield losses, including by speeding up and expanding conscription. In particular, senior American officials have urged Kyiv to expand its draft to younger men aged 18 to 25, who are now exempt.

“Even with the money, even with the munitions, there have to be people on the front lines to deal with the Russian aggression,” Secretary of State Antony J. Blinken said in Brussels last week.

While Ukraine’s battlefield losses are dwarfed by Russia’s — estimated at up to 400,000 irreplaceable losses — military analysts warn they are less sustainable for Kyiv because it has faced greater difficulties than Russia in replenishing its ranks.

Russia, trying to avoid a round of national conscription that could anger citizens, has sought to recruit heavily from prisons and volunteers. Ukrainian and Western officials also estimate that North Korea sent about 10,000 soldiers to help Russia this year, as the countries leaders developed closer ties.

Many Parisians can tell you exactly what they were doing when they heard that Notre-Dame was burning five years ago.

Many of them instinctively rushed toward the building, and lined the Seine River to watch in horror as flames devoured the ancient lead roof, sending the 19th-century wooden spire tumbling down, punching holes through the vaults and burning the pews below.

Some dropped to their knees and prayed, but the cathedral is not just a sanctuary for the faithful. Nor — its millions of visitors a year notwithstanding — is it just a tourist attraction. Notre-Dame, as the crowds of stricken Parisians testified to on that April 2019 day, is the heart of their city, part of the essential fabric of its identity, and a part of them.

Notre-Dame is, however, first and foremost a church, and on Sunday evening, worshipers returned there as its first regular Mass was celebrated below the soaring stone arches — the old ones indistinguishable from the new.

“Five years after its destruction, here it stands again, ready to welcome the prayers of the faithful, to welcome the heart, the cry of the heart of all those who come here from all over the world,” Msgr.Olivier Ribadeau Dumas, rector of the cathedral, declared in his opening remarks. “Fire has not conquered stone, despair has not conquered life.”

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Early in Russia’s war against Ukraine, Mykola Kulichenko endured an ordeal. He was abducted as a civilian, survived a Russian execution attempt by a stroke of luck and then climbed out of his own grave by pushing through the dirt heaped above him.

His brothers died beside him, but Mr. Kulichenko had turned his head at the last moment and a bullet passed through his cheek, leaving a hole but not causing life-threatening wounds.

His case elicited widespread shock and sympathy in Ukraine — but it did not shield him from Ukraine’s mobilization system. He received a draft summons in October.

Mr. Kulichenko has used his second lease on life to care for his elderly father and return to raising ducks and chickens on a farm in northern Ukraine. But he said he still has trouble sleeping, as he flashes back to being shot and buried alive then finding his way home with his body covered in bruises and his cheek bleeding and tremendously swollen.

Given the trauma of his ordeal, he doesn’t think he should be drafted into the army. “It was very hard to climb out of my grave,” he said.

“What would it change if I go” to the trenches now, he said, claiming that his presence would have no impact on the fighting. “I would take my life to the front and leave it there, for nothing.”

The summons of Mr. Kulichenko, who is 35, underscores the unpredictable and lopsided mobilization system in Ukraine that leans heavily on recruiting older men.

The policies have drawn criticism from the Biden administration, which has said Ukraine should expand its draft to younger men aged 18 to 25, who are now exempt, to defend hundreds of miles of front line. The need for soldiers is now more acute than the need for weapons, American officials have said.

Ukrainian officials say they cannot draft men in their late teens and early 20s without risking demographic shortfalls in the future, and they have pushed back against the American criticism.

“Ukraine cannot be expected to compensate for delays in logistics or hesitation in support with the youth of our men,” Dmytro Lytvyn, a communications adviser to the president, wrote recently in a post on X. It was another swipe at the pace of Western weapons support, which Ukraine views as tepid and overly cautious.

Mr. Kulichenko’s experience also points to the difficulty Ukraine has had in calibrating the rules governing draft exemptions. He became eligible for recruitment after rule changes last spring eliminated some exemptions for hardship, including for those caring for ailing relatives.

Like a game of Whac-a-Mole, each change knocks out some who enjoyed exemptions while adding others who had not — with civilians left to argue over which hardship was more deserving.

The changes to the law were intended to crack down on draft dodgers who abused the mobilization system by claiming hardship when little actually existed, a practice abetted by corruption in the draft operation.

With the loopholes supposedly plugged, recruitment officials stepped up the draft through the summer. Ukraine does not disclose figures, but military analysts have said an initially promising flow of recruits for the army has since tapered off. Fewer men are entering basic training, and many of them are old or in poor health, military commanders say.

Ukraine plans to draft an additional 160,000 men in the “near future,” the secretary of the National Security and Defense Council, Oleksandr Lytvynenko told Parliament late last month. This number would restore units to 85 percent of their full strength, he said.

But reaching deeper into the pool of older men risks filling the ranks with less motivated and healthy soldiers. Even now, none of the brigades in combat are fully staffed, said Maj. Maksym Zhorin, a commander in the 3rd Assault Brigade. Of the new soldiers turning up, he said, “the quality of personnel has significantly deteriorated recently.”

Ukraine, meanwhile, is falling back at two locations on the front inside the country, in the eastern Donbas region and near the town of Kupiansk in northeastern Ukraine, and it has lost about half of the territory captured in an incursion into the Kursk region of Russia in August.

“We are truly on the verge of a military catastrophe,” Yevhen Dykyi, a military veteran and commentator on the war for Ukrainian media, told radio NV. It is not because of mistakes by the army, he said, but because of the failure to draft enough soldiers.

But aggressive mobilization efforts, mostly aimed at older men in rural areas, have led to a backlash in society. Women have blocked roads to prevent recruitment officials from searching for draft dodgers in some western Ukrainian villages.

Men have slipped across the borders to Europe to avoid the draft, sometimes swimming across rivers. Others simply remain at home, lest they get picked up at a checkpoint or other location.

Parliament has been considering a partial swing of the pendulum back — introducing several overhauls to reduce draft evasion and desertion by restoring exemptions and granting draftees more choice in how they serve. Men are now sometimes allowed to choose or change the units in which they serve, for example.

An amendment passed in Parliament in a first reading on Nov. 20 would grant deferments to civilians whom the Russians had arrested earlier in the war and to those who lost close relatives in the fighting.

If signed into law, Mr. Kulichenko could qualify on both points, though under current rules he is still eligible for the draft.

The issue of whether war injuries should merit an exemption from future service has been a divisive one in Ukraine. Men have returned to serve after suffering more grievous injuries than Mr. Kulichenko. Some have voluntarily returned to service even after their legs or arms were amputated. Such dedication is praised by Ukrainians who view their lives and homes depending on holding back Russian soldiers.

Russians arrested Mr. Kulichenko and his two brothers in March 2022 in their hometown, Dovzhyk, north of Kyiv. The dynamic in the war was the opposite of today — the Russians were retreating from northern Ukraine. The brothers were suspected of planting or helping to plant a roadside bomb that killed several Russian officers, Mr. Kulichenko said. He denied any role in the incident.

The brothers were held for three days in an abandoned sawmill where they were interrogated and severely beaten. With the Ukrainian Army approaching, Mr. Kulichenko said, the Russians decided to shoot the brothers to eliminate evidence of the torture. His ordeal was reported at the time by The Wall Street Journal and later taken up in a war crimes prosecution in Ukraine, in which Russian soldiers were tried in absentia.

Russians loaded the brothers in a truck, drove them into the forest, lined them up beside the grave and opened fire. A bullet passed through Mr. Kulichenko’s cheek and he fell to the ground. He lay still as the soldiers piled on dirt, then clambered out after they left.

The draft summons arrived in October. He said he understands the army “lacks people and that is why they take everyone.”

He has not responded to the letter by appearing at a draft board, and said he does not intend to. He does not want to fight in the war, given what happened to him, he said.

“I didn’t get over it,” he said.

Oleksandra Mykolyshyn contributed reporting.