The Israeli military’s rescue of a hostage from an underground tunnel in the Gaza Strip on Tuesday highlighted one of the biggest remaining impediments to Prime Minister Benjamin Netanyahu’s goal of eradicating Hamas: the enclave’s vast and complicated subterranean network that shelters many of the militant group’s remaining leaders.

Israel’s military said on Tuesday that it had rescued Farhan al-Qadi, a member of Israel’s Bedouin Arab minority who was abducted on Oct. 7, from an underground Hamas tunnel in southern Gaza. According to two senior officials who spoke on the condition of anonymity because they were not authorized to talk to reporters, Israeli forces appear to have found Mr. al-Qadi by chance as they were combing through a tunnel network for Hamas fighters.

It was the second time in two weeks that Hamas’s network of tunnels featured prominently in Israel’s accounts of hostage recovery efforts, shining some light on a mostly unseen aspect of the war that looms large for the country’s military and government officials. Last week, Israeli troops said they had recovered the bodies of six hostages hidden behind concrete lining in an underground route connected to a 10-meter-deep tunnel shaft.

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A public inquiry into the case of Lucy Letby, a British neonatal nurse convicted of killing seven babies, has come under fire from scientific and medical experts who have called for it to be delayed or broadened to consider whether the deaths could have been caused by other factors.

The inquiry, set to begin on Sept. 10, will cast a fresh spotlight on one of the most haunting murder cases in recent British history. Conscientious and well liked by her colleagues, Ms. Letby was found guilty of killing seven infants, and trying to kill seven others, in a busy public hospital in 2015 and 2016.

Ms. Letby, 34, was sentenced to life in prison last year and her requests for appeals have so far been denied. But questions about the handling of the investigation and the evidence used to convict her have grown harder to ignore, with prominent experts in statistics and neonatal medicine arguing that both were gravely flawed.

Under the terms of its mandate, the inquiry will not scrutinize those questions. Instead it will hold hearings to probe the experiences of the families of the babies who died and the conduct of nurses, doctors, and other health workers at the Countess of Chester Hospital, southeast of Liverpool.

Led by Kate Thirlwall, an appeals court justice, the inquiry aims to determine “whether suspicions should have been raised earlier, whether Lucy Letby should have been suspended earlier, and whether the police or other external bodies should have been informed sooner about suspicions about her.”

The thornier question — whether Ms. Letby might have been wrongfully convicted — falls beyond the scope of the inquiry, which was announced in 2023 by the health secretary in the last Conservative government.

The inquiry’s narrow scope prompted 24 experts, who emphasized that they had no connection to Ms. Letby or her family, to send a letter last month to the current health secretary, Wes Streeting, and the justice secretary, Shabana Mahmood.

In excerpts provided to The New York Times by a representative of the signatories, they wrote, “While we acknowledge the gravity of the convictions against Ms. Letby, our focus is on the broader implications for patient safety, health-care management and the potential for miscarriages of justice in complex medical cases.”

“Possible negligent deaths that were presumed to be murders could result in an incomplete investigation of the management response to the crisis,” they added, in a letter first reported by The Guardian. “Our goal is not to re-litigate the Letby case, but to ensure that the Thirlwall inquiry is positioned to conduct the most thorough and beneficial investigation possible for the future of neonatal care in the UK.”

Among the signatories are Peter Elston, a fellow of the Royal Statistical Society, and Gillian Tully, an expert in forensic science at Kings College London who served as the forensic science regulator for England and Wales. The signatories declined to release the full letter, saying it was intended to be private.

Medical experts have argued that other factors — including staff shortages, crowded conditions in the ward, poor equipment, or management problems — could have contributed to the abnormally high number of babies dying or becoming seriously ill in the unit where Ms. Letby worked. The National Health Service was under acute pressure during this period, after years of constrained budgets and understaffing.

Statisticians have criticized the investigation for concluding that because Ms. Letby was on duty during a cluster of these incidents, she must have been responsible for them.

The case hinged on her being held responsible for administering an overdose of insulin to two babies, but both survived, and several medical experts said the test results used to suggest insulin had been artificially administered were not reliable as evidence of a crime.

There were no witnesses to Ms. Letby killing or mistreating babies under her care, and she has denied murdering anyone. While her lawyers tried to discredit the prosecution’s evidence, they did not present their own evidence.

Phil Hammond, a retired doctor in the National Health Service who has written about the case as medical correspondent for Private Eye magazine, pointed out that the defense only appointed one expert and never called him. “Unsurprisingly, the evidence was very one-sided,” he said. The prosecution, he added, “were shooting at an open goal.”

Mr. Hammond has signed a separate open letter to Prime Minister Keir Starmer, which calls for a “full forensic review of the evidence used in the Letby case.” He said he was not sure whether Ms. Letby did what she was convicted of, but he does not believe she got a fair trial, a position held by a number of other people involved in the case. That could pose a challenge to an inquiry that was created on the basis that she was guilty.

Ms. Letby has been convicted twice: in August 2023, on seven counts of murder and six counts of attempted murder; and last July, on a single count of attempted murder, in a retrial after the jury did not reach a verdict on that charge in the first trial.

News coverage of the case included sensational details like her anguished handwritten notes. She wrote, “I killed them on purpose because I’m not good enough to care for them,” and in capital letters, “I AM EVIL I DID THIS.” Yet on the same piece of paper she had also scrawled: “I haven’t done anything wrong,” “I feel very alone + scared,” and “slander discrimination.”

Reporting on the case was cut off at critical junctures because of restrictions under English law on news that could prejudice a jury. Last September, the restrictions were reimposed after the public prosecutor for England and Wales announced it would seek to retry the attempted murder charge. They have since been lifted.

In May, The New Yorker published a highly critical 13,000-word investigation of the case. The magazine’s publisher, Condé Nast, blocked access to online readers in Britain, for fear of being held in contempt, which can be punished with a fine or prison sentence, although the magazine was available in print and on the magazine’s app. British papers, like The Guardian and The Times of London, have since run articles questioning the evidence, as have broadcasters.

For all the concerns being raised, however, some doubt the new Labour government will delay or expand the scope of the inquiry.

“There isn’t a political energy or head space to do it,” Mr. Hammond said. “It would be so embarrassing if the biggest baby-killer case in British history was found to be unsound.”

The White House national security adviser, Jake Sullivan, met on Thursday with China’s leader, Xi Jinping, and held rare talks with a top Chinese military official in a sign that the two countries are communicating at senior levels despite tensions over the South China Sea and Taiwan.

Mr. Sullivan’s meeting with Gen. Zhang Youxia, vice chairman of China’s Central Military Commission, was the first in years between a senior American official and a vice chair of the commission, which oversees China’s armed forces and is chaired by Mr. Xi. In 2018, Jim Mattis, who was the U.S. defense secretary at the time, met with Gen. Xu Qiliang, who held the vice chair position.

It was the latest effort by the two powers to keep communication channels open even as disputes grow over national security, trade and geopolitics. On the military front, the United States has argued that more open communication is necessary to prevent accidents between the two countries’ warplanes and navy ships as they regularly patrol contested areas like the Taiwan Strait and the South China Sea.

“A meeting with Zhang Youxia is very significant, and an indication that China is prepared to meaningfully re-engage with the Department of Defense,” said Drew Thompson, a visiting senior research fellow at the Lee Kuan Yew School of Public Policy at the National University of Singapore. “Beijing views the military-to-military relationship as an important political indicator of the overall relationship, which differs somewhat from the U.S. perspective, which sees it as a more pragmatic channel to reduce risk.”

Mr. Sullivan’s meeting with General Zhang, which was held at the headquarters of China’s People’s Liberation Army, came on the final day of his three-day visit to Beijing to bolster the Biden administration’s bid to manage competition with China.

China and the United States have been locked in a rivalry for global influence and have seen tensions rise over a raft of issues, including China’s territorial claims in the South China Sea, its tacit support for Russia’s war in Ukraine, and the flood of Chinese electric vehicles and solar panels onto global markets.

“We believe that competition with China does not have to lead to conflict and confrontation — the key is responsible management through diplomacy,” Mr. Sullivan said at a news conference after meeting with Mr. Xi.

Even as the visit was a chance for both nations to reassure the world that they were working to lower the risk of conflict between them, it was clear that they were still fundamentally divided on strategic issues. China has rejected Washington’s framing of the bilateral relationship as being defined by competition, a stance Mr. Xi highlighted at the top of an official summary of the meeting.

“First of all, we must answer the general question of whether China and the United States are rivals or partners,” Mr. Xi told Mr. Sullivan. China’s intentions were “above board,” he said, and his country was committed to “peaceful development.” He said he hoped that the United States would work with China to “find a correct way for the two major countries to get along.”

Mr. Sullivan told reporters that the Biden administration’s priorities in its final months included greater communication between their militaries and more cooperation to tackle the fentanyl crisis in the United States.

He also elaborated on discussions about a potential meeting between President Biden and Mr. Xi, noting that both leaders would likely attend the Asia-Pacific Economic Cooperation summit in Peru and the Group of 20 Leader’s Summit in Brazil, to be held in mid-November.

“It would only be natural for them to have the chance to sit down with one another,” Mr. Sullivan said.

He also spoke briefly about Vice President Kamala Harris, who is now the Democratic Party’s presidential candidate, and her perspective on China.

“She shares President Biden’s view that responsibly managing this competition, so it doesn’t veer into conflict or confrontation, is essential,” Mr. Sullivan told reporters, noting that Ms. Harris has met Mr. Xi and also China’s second-highest official, Premier Li Qiang.

Earlier in the day, General Zhang told Mr. Sullivan that the world expected the two countries to “maintain stability in the military and security fields,” according to a statement released by China’s defense ministry. He also reiterated China’s opposition to American support for Taiwan, the island democracy that Beijing claims.

“China demands that the United States stop military collusion between the United States and Taiwan, stop arming Taiwan, and stop spreading false narratives involving Taiwan,” the general said, according to the official statement.

Mr. Sullivan later said that having a chance to speak in person with General Zhang had made a difference.

“The meeting with Vice Chairman Zhang was very important — there is no substitute for actually being able to sit across the table not just with the vice chairman but with his whole team, to be able to hear from them their perspective on critical issues,” he said.

On Wednesday, Mr. Sullivan and China’s most senior diplomatic official, Wang Yi, said their countries’ top military commanders in the region would hold a video call at some point.

Mr. Thompson said such a call could help reinvigorate lower-level dialogue that used to take place more frequently in the past. Those meetings, he said, allowed military personnel to discuss aerial and maritime maneuvers in greater detail to prevent accidents.

Washington is also concerned about encounters between China and U.S. allies that could draw American forces into a confrontation. That includes the most recent standoff between the Philippines and China near a disputed atoll, Sabina Shoal, where Chinese coast guard vessels have rammed Philippine ships and targeted them with water cannons.

“The order of the day should be de-escalation” in the South China Sea, said Mr. Sullivan, who, during his talks in Beijing, raised America’s commitment to defend the Philippines as a treaty ally.

“Nobody is looking for a crisis — not the Philippines, not the United States and, we hope, not the P.R.C.,” he said, referring to the People’s Republic of China.

Such regional tensions have led to chilly relations between the Pentagon and the Chinese military over the past several years. China suspended military-to-military communications in 2022 after Nancy Pelosi, who was speaker of the House at the time, visited Taiwan. They were restored in December when President Biden’s senior military adviser, Gen. Charles Q. Brown, held a videoconference call with his Chinese counterpart, Gen. Liu Zhenli.

Ukraine’s military said on Thursday that it had struck two more Russian oil depots, pressing ahead with a campaign of attacks against a sector vital to Moscow’s war effort.

The strikes coincided with accelerated lobbying by Ukraine’s political leaders for permission to use weapons supplied by allies in NATO to strike targets deep inside Russia, as Kyiv seeks to bring the pain and hardship of war home to Russia.

The Ukrainian military said it launched an attack that caused a fire on Wednesday at the Atlas oil depot in the Rostov region, which borders eastern Ukraine. The governor of the region, Vasily Golubev, reported a fire at an oil depot and said that four drones had been shot down.

Ukraine also struck an oil depot in Russia’s Kirov region, which is roughly 800 miles from the Ukrainian border, northeast of Moscow; and an artillery depot in Voronezh region, which borders Ukraine, the military’s general staff said.

The Russian governor of the Kirov region, Aleksandr Sokolov, said in a post on Telegram that an oil facility there had been set on fire on Wednesday. Two drones were shot down, while three others crashed, he said. The governor of the Voronezh region, Aleksandr Gusev, also reported a drone attack, but said in a post on Telegram that no damage was caused.

The claims could be independently confirmed.

For months, Ukraine has conducted attacks using exploding drones against Russian infrastructure, in particular oil facilities, hoping to slow an offensive by Moscow’s forces. Russia has nevertheless advanced toward the city of Pokrovsk, which is an important transport and logistics hub in eastern Ukraine.

In Kyiv, explosions from a Russian drone attack rattled buildings overnight, the third time this week that Moscow had launched an aerial attack against the Ukrainian capital. Ukraine’s Air Force said it had shot down 60 drones and two missiles, but the attack was smaller than on Monday, when strikes hit many regions.

Moscow’s aerial campaign, which has frequently targeted Ukraine’s power grid, aims to cripple the country’s ability to stave off Russia’s full-scale invasion and deepen the hardships of war for Ukrainian civilians.

But the government in Kyiv has attempted a riposte with its own series of attacks, including the surprise offensive over the border into Russia’s Kursk region that began earlier this month.

That incursion has been accompanied by calls from Ukrainian officials for its allies to ease restrictions on the use of the missiles they have given to Kyiv that prohibit striking deep inside Russia with them.

A member of Ukraine’s Parliament said in June that the armed forces had used a rocket system supplied by the United States to hit a military facility in Russia’s Belgorod region, which borders Ukraine.

The country also used American-supplied munitions and vehicles in its Kursk incursion. Pentagon and State Department officials have said that use of American-supplied weapons and munitions did not violate U.S. policy.

President Volodymyr Zelensky late on Wednesday urged the country’s allies from NATO to give his country more weapons and greater latitude to use them against Russia itself. True unity with NATO partners, he said in a speech overnight, would mean permission to do long-range strikes.

“We continue to insist that their determination now — lifting the restrictions on long-range strikes for Ukraine now — will help us to end the war as soon as possible,” he said. Earlier this week, the defense minister, Rustem Umerov, said Ukraine wanted to be able to strike logistics points and military airfields.

Russia has threatened a grave response to any attacks on its soil with Western weapons. Some of Ukraine’s allies have argued that their use risked a direct confrontation between NATO and Russia, a nuclear-armed nation. So far that grave response has not materialized.

Earlier this summer, the Biden administration gave permission for Ukraine to conduct limited strikes inside Russia with American-made weapons — but only in Russian territory near northeastern Ukraine and for defensive purposes.

A wide range of significant targets that underpin Moscow’s campaign could be within reach of Ukraine’s longer-range weapons, the Institute for the Study of War, a think tank based in Washington, said in a recent report.

Diplomatic outreach has been a critical component of the Ukrainian government’s response to Russia’s invasion and on Wednesday, Mr. Zelensky spoke by telephone with Prime Minister Benjamin Netanyahu of Israel.

Mr. Zelensky joined other international leaders in expressing strong support for Israel after a deadly attack led by Hamas on Oct. 7, but the two men had not spoken for nearly a year, according to a report by Kan, the Israeli public broadcaster.

They discussed the situation in the Middle East and the recent Russian attacks on Ukraine as well as other topics, the report said. Mr. Netanyahu also expressed support for Ukraine’s territorial integrity, according to Serhiy Nikiforov, Mr. Zelensky’s spokesman.

The government in Kyiv has also attempted to corral diplomatic support for its own peace plan, which would involve a complete Russian withdrawal from Ukrainian territory. This week, Mr. Zelensky said he planned to present a “plan for Ukraine’s victory” to President Biden in September.

Ukraine’s incursion into the Kursk region is part of the plan, along with further financial measures to force Moscow to end the war, Mr. Zelensky said. He gave few other details.

The European Union has presented itself as a champion for promoting gender equality, adopting rules requiring companies to increase the number of women on their boards and pushing employers to address the gender pay gap.

So when Ursula von der Leyen, the president of the European Commission, asked recently for member countries to nominate both male and female candidates for leadership positions within the 27-member bloc’s executive arm, it was seen as an attempt to apply that vision to its own halls. The problem is, few have listened.

Only five countries — Sweden, Finland, Spain, Portugal and Croatia — have put forward female candidates ahead of a Friday deadline. Seventeen countries have nominated only men for their commissioner posts. (Three countries have yet to submit names.) Each country gets one leadership slot.

It’s possible that some countries could still change their nominees ahead of the deadline. But the current slate of nominees suggests that the European Commission’s leadership team will likely be composed mostly of men for the next five years — and analysts said the public snub of Ms. von der Leyen’s request signals her leadership could be weakened.

“It’s not a small thing, asking for gender balance and clearly not getting it,” said a senior European official. “It’s not just one, two countries.” Speaking on condition of anonymity because the process was ongoing, the official said that indicated Ms. von der Leyen’s relations with member states would be more difficult.

Ms. von der Leyen, a conservative German politician, secured a second five-year term in a vote last month.

“National political leaders are certainly less willing, this time around, to adhere to this type of request,” said Jacob Kirkegaard, a senior fellow at the German Marshall Fund. He said that Ms. von der Leyen was able to get more cooperation in her first term because the E.U. was dealing with Covid and other crises, but will likely now need to become a more traditional “wheeling-and-dealing commission president.”

The commission’s leadership team creates and implements policies affecting 450 million European citizens.

“The E.U. as an international organization and as a political body often makes claims to being a trailblazer in the area of gender equality,” said Roberta Guerrina, a professor and researcher of E.U. gender politics at Bristol University. “Therefore, walking the talk becomes really important, and having equal representation on decision-making bodies is the starting point.”

Two of the top 27 positions in the European Commission have already been filled and are held by women: Ms. von der Leyen, the president, and Kaja Kallas, the bloc’s top diplomat and a former prime minister of Estonia.

For the rest of the leadership roles, the remaining 25 member states nominate officials to serve as commissioners, who act much like national ministers and oversee areas like health, economy or trade for the bloc. From those nominees, Ms. von der Leyen then drafts a list of candidate commissioners, one for each member country. The proposed appointments require approval from the European Parliament.

When Ms. von der Leyen first became European Commission president five years ago, she made the same request for E.U. capitals to nominate a man and a woman for commission posts. She ended up forming the most gender-equal group of leaders in the bloc’s history, with 12 female commissioners and 14 male commissioners.

“What she’s trying to do with her request this time around is to actually institutionalize that process,” Dr. Guerrina said. “If you just expect employers or governments to just act on their own accord based on best practice, progress is going to be incredibly, incredibly slow.”

Women are underrepresented within E.U. institutions, but significant progress has been made in recent decades. Two of the bloc’s three top bodies are led by women — Ms. von der Leyen and Roberta Metsola, head of the European Parliament.

It’s difficult to say with certainty why so many countries have ignored Ms. von der Leyen’s request.

Simon Harris, Ireland’s head of government, said last month that he takes gender equality “seriously” but that his country was only nominating Michael McGrath, its former finance minister, because he was the best candidate. Mr. Harris said he was not willing to nominate a woman to compete against Mr. McGrath in the selection process.

Since there is no legal requirement for countries to submit both a male and a female candidate, Ms. von der Leyen’s options to boost female representation are limited. Politico reported on Wednesday that she was making a last-ditch effort to persuade some countries to submit alternate nominees. A European Commission spokesman declined to comment on the process, saying it was ongoing.

Gender equality researchers say female representation within the E.U.’s top echelons is critical so that policies are crafted in ways that reflect the needs and challenges that women face. It’s particularly important now, said Georgie Bradley, a spokeswoman for the European Institute for Gender Equality.

The percentage of female parliamentarians in the legislative term that began in July fell to 38.7 percent, the first ever decrease, compared to the last five-year term, when more than 42 percent of the 720 members of the European Parliament were women, according to an analysis that the agency will publish next month.

“There is a slip,” Ms. Bradley said, therefore you must “always keep gender equality in mind.”