President Volodymyr Zelensky of Ukraine agreed in a Wednesday phone call with President Trump to accept Russia’s offer of a mutual pause in attacks on energy targets for 30 days as a step toward a broader cease-fire.

It was not immediately clear how or when a pause in strikes on certain targets would take hold. “Everything will continue to fly,” Mr. Zelensky said in a later news conference from Finland, until “there is an appropriate document” negotiating terms. He added that Russian drones were in the air in Ukraine as he spoke.

During the call between Mr. Trump and Mr. Zelensky, the American president floated the idea of the United States possibly taking control of Ukrainian power plants, according to an official U.S. statement; it was a new idea that Ukrainian energy experts said was probably unworkable.

Mr. Zelensky later elaborated during his news conference that he felt he faced “no pressure” from Mr. Trump about that idea, saying it was limited to one plant. He added that the call with Mr. Trump was “the most substantive in recent times” and that the list of targets protected from strikes in a partial cease-fire could be expansive.

But any agreement restricted to energy targets between Mr. Zelensky and President Vladimir V. Putin of Russia would leave a wide chasm between their positions on how the war could end. And Mr. Zelensky has characterized some of the Russian leader’s proposals as stalling tactics as he maneuvers for military advantage and the best possible deal from the American president.

A joint statement from Mr. Trump’s national security adviser, Michael Waltz, and the secretary of state, Marco Rubio, said technical teams would meet in Saudi Arabia “in the coming days” to discuss broadening the cease-fire on energy sites to one covering activity in the Black Sea, “on the way to a full cease-fire.”

Wednesday was the first time Mr. Trump and Mr. Zelensky had spoken since a dramatic confrontation in the Oval Office last month.

During that meeting, Mr. Trump and Vice President JD Vance berated Mr. Zelensky for showing insufficient gratitude for American support — most of it delivered under President Joseph R. Biden Jr. The Trump administration temporarily suspended all military assistance and intelligence sharing with Ukraine in the aftermath of the meeting, and Mr. Zelensky has since sought to smooth over relations.

Wednesday’s statements from Mr. Zelensky, Mr. Trump and his national security officials suggested that efforts to make amends had produced results.

Mr. Trump said his conversation with Mr. Zelensky had been “very good” and lasted about an hour. The joint statement from Mr. Waltz and Mr. Rubio said the talk had “significantly helped in moving toward ending the war.”

Mr. Zelensky called the conversation “positive, very substantive and frank,” making clear that he had thanked Mr. Trump for America’s support.

But the idea of the United States owning any of Ukraine’s electrical and nuclear facilities could present myriad difficulties, and the two sides did not seem in sync about what plants were at issue.

Mr. Zelensky suggested the idea was limited to the Zaporizhzhia nuclear power plant, Europe’s largest, which is currently controlled by Russia.

“The question was exclusively about the station under temporary occupation,” Mr. Zelensky said.

The statement from Mr. Rubio and Mr. Waltz, however, referred to “Ukraine’s electrical supply and nuclear power plants” and said the United States could be “very helpful in running those plants with its electricity and utility expertise.”

In the next sentence, they suggested that Ukraine should sell or transfer ownership of those facilities — plural — to the United States, much as they have demanded a partial interest in Ukraine’s minerals. And they offered the same argument as in the minerals case: that the American stake would make Russia less likely to attack them.

“American ownership of those plants would be the best protection for that infrastructure support for Ukrainian infrastructure,” Mr. Rubio and Mr. Waltz said.

Olga Kosharna, a Ukrainian nuclear energy expert, said such plants cannot be privatized under Ukrainian law. Other experts were also skeptical of the plan, but noted that U.S. involvement could help improve management at the plants.

Mr. Putin rejected an earlier proposal for a comprehensive 30-day cease-fire covering land, sea and air. Under pressure from Mr. Trump, Ukraine’s government agreed to that idea during a meeting with U.S. officials in Saudi Arabia earlier this month, despite Kyiv’s deep misgivings about bargaining with Mr. Putin.

Mr. Putin raised multiple objections to that idea, however, and countered with the narrow plan to protect energy sites.

Many analysts argue that such an agreement would mainly benefit Moscow, whose oil refineries have come under increasingly heavy long-range Ukrainian attacks. And while Russian strikes have wreaked havoc on Ukraine’s energy supplies, Ukraine has learned to adapt over three years of war and will depend much less on heat in the coming weeks than it did in winter.

Insisting that the broader talks are “very much on track,” Mr. Trump wrote in a social media post on Wednesday that his talk with Mr. Zelensky was “based on the call” he had with Mr. Putin the day before, “in order to align both Russia and Ukraine in terms of their requests and needs.”

Mr. Trump’s efforts to broker a deal have put Mr. Zelensky in an awkward position. The Ukrainian leader fears that in his eagerness for a deal with Mr. Putin, Mr. Trump might force Ukraine into unwanted concessions. Mr. Zelensky also finds himself targeted by Trump officials and allies who have accused him of obstructing peace and who have threatened to force him from office.

Mr. Zelensky has little leverage, given that U.S. military and economic support is critical to his country’s ability to fend off the Russians, so he has done his best to accommodate Mr. Trump. On Wednesday, the Ukrainian president said that the limited cease-fire would need U.S. monitoring to work.

“Just the assertion and the word of Putin that he will not strike energy sites is too little,” Mr. Zelensky said. “War has made us practical people.”

Ukraine would prepare a list of sites to be protected, he said at a news conference in Helsinki alongside Finland’s president, Alexander Stubb. If monitoring confirmed that “Russia doesn’t strike our objects,” Mr. Zelensky added, “we will not strike theirs.”

Underscoring the lack of trust between Ukraine and Russia, the two countries traded accusations on Wednesday about attacks against each other’s energy infrastructure.

Ukraine’s European allies have cautiously welcomed any moves toward a cease-fire, while pledging further support for Kyiv and echoing concerns about Russia’s conditions.

“It’s a yes or a no: No buts, no conditions,” Mr. Stubb said. “Ukraine accepted a cease-fire without any form of conditions. If Russia refuses to agree, we need to increase our efforts to strengthen Ukraine and to ratchet up pressure on Russia.”

It was clear by the end of the day that the global diplomacy around Ukraine’s fate would continue at an intense pace.

Mr. Zelensky spoke again from Finland on Wednesday evening, in an online discussion that was briefly interrupted when he received a call from yet another world leader. President Emmanuel Macron of France was on the line. Mr. Zelensky told him he was busy and would have to call him back.

David E. Sanger contributed reporting from Washington; Constant Méheut from Kyiv, Ukraine; Anastasia Kuznietsova from Mantua, Italy; and Johanna Lemola from Helsinki.

From Brussels to Berlin, leaders across Europe are getting ready to spend hundreds of billions to rebuild their armies. The spending, they say, is necessary to prepare Europe for the dangers of a world where the United States no longer guarantees its security.

But many of them are also hoping that the surge of money will have another important effect: revitalizing the continent’s slumping industrial sector and opening a new front for economic growth.

That connection between defense investment and competitiveness is one of the topics European leaders are likely to discuss when they meet in Brussels on Thursday, after the European Commission publishes a long-awaited paper on the future of European defense on Wednesday.

“Economic strength and Europe’s plan to rearm are two sides of the same coin,” Ursula von der Leyen, president of the European Commission, said in a recent speech, calling the potential investments a “powerful tailwind for important industries.”

But whether that will be the case is far from certain, and the challenges to Europe’s actually making it happen are enormous.

While there is a growing consensus that new military spending is likely to offer some boost to European economies in the near term, just how much will depend on how well that money is spent and where.

Most European economies have relatively modest defense industries, though France and Germany in particular are seeking to grow theirs. For decades, Europe has depended significantly on imports of American arms and equipment, particularly when it comes to the most sophisticated weapons. That makes the continent not particularly well suited to absorb new military spending immediately.

But European leaders are keen to change that, in order to keep tighter control over their own security and to best reap the economic impact from that investment.

President Emmanuel Macron of France is pushing allies, including Germany, to buy French missile-defense systems instead of American ones. Portugal’s defense minister said last week that the country might replace aging fighter jets with European ones, not American-made F-35s, citing concerns over the Trump administration’s embrace of Russia.

The European Union’s recently unveiled 150 billion euro loan program — about $163 billion, meant to finance shared military development — will prioritize European-made products, officials announced on Wednesday. Member states must ensure that 65 percent of the costs of what they buy comes either from within the E.U. or from partners including Ukraine and Norway.

But building out Europe’s modest military industries to meet those ambitions will take time.

Friedrich Merz, Germany’s likely incoming chancellor, laid out the challenges to lawmakers on Tuesday, before Germany’s lower house of Parliament voted to loosen constitutional limits on debt to allow billions more in spending to revamp the country’s military. The measures must now pass the upper chamber and survive legal challenges before becoming law.

“Now we need to rebuild defense capabilities, in part from scratch, with a technology-driven defense and procurement strategy, with automated systems, with independent European satellite surveillance, with armed drones and with many modern defense systems and, above all, with reliable and predictable orders that should go to European manufacturers whenever possible,” Mr. Merz said.

European nations have increased spending on defense by nearly a third since 2021. But even combined, their annual military budgets remain less than half of the United States’. Defense industries employed just under 600,000 Europeans last year. By comparison, automobile manufacturers alone employed more than three million.

In some cases, like tanks and missile batteries, Europe will need to scale up existing industries or repurpose other industrial production lines. In others — including drone technology and some of the most cutting-edge weapons and military support equipment — Europe will need to build its own rivals quickly to compete with American players. Defense officials caution it could take years to pull that off, if not a decade.

And there is a risk that when European nations buy close to home, they will want to buy domestically rather than from Germany or France — duplicating efforts across the bloc. Europe already has some redundancy problems in defense. Ukraine, for example, has been sent at least 17 kinds of howitzers, not all of which use the same type of shell.

If Europe’s new spending ends up being duplicative, both the economic and strategic benefits could be muted.

That is why some economists caution that the economic lift, while likely, might not be enough to buffer European governments against the populist backlash they have faced in recent years.

But if the European Union can add new industries with coordinated investment and purchasing, then the growth effects could be significant.

They might even be enough to help aging European countries temper a downward spiral of shrinking workforces and plunging investment, spurring new technologies that would spill over into civilian sectors and providing a more lasting benefit.

Much depends on how the new spending plans play out.

The philosophy, at the moment, appears to start with spending big — and staying close to home. In Brussels, E.U. officials have made clear that they want to build up defense production abilities across their 27-member bloc. To catalyze investment, they have pitched a €150 billion loan program.

They have also proposed loosening European fiscal rules so that individual nations will be able to spend more, which they estimate could unleash as much as €650 billion, more than $710 billion, in additional spending. Whether that much spending actually happens will hinge on whether national governments are willing to take on more debt for military spending.

Even with the challenges of buying local, many economists think that European growth as a whole will see some benefit from the defense buildup. Goldman Sachs estimated a modest bump in the eurozone in each of the next three years, with the largest benefit in 2027.

The Goldman economists upgraded their growth estimates in part because of the German plan to ease debt limits. But others tempered expectations.

The German military spending plan “is really about security,” said Clemens Fuest, an economist who is the president of the ifo Institute in Munich, and who helped advise Mr. Merz.

“It’s good for the country because we want to avoid war in Europe,” Mr. Fuest said in an interview. But, he added, “It’s not good in terms of, ‘It’s going to create more growth,’ or anything.”

Still, at a time when German automakers and their suppliers have shed some 46,000 jobs since 2019, some Germans wonder if it may be time to turn idled automotive factories into cutting-edge plants for tanks or drones.

The German arms maker Rheinmetall has already taken a lead role in scaling up the country’s weapons-production capacities. It has provided new jobs to dozens of workers from one of Germany’s struggling auto suppliers, Continental AG. It has also been in talks with Volkswagen about the possibility of taking over an underperforming factory near Osnabrück.

“If German taxpayer money is being spent, then we need to create German jobs,” Armin Papperger, Rheinmetall’s chief executive, told reporters last week, adding that he expected Rheinmetall alone to add 10,000 jobs in Germany over the next two years.

That growth may be felt beyond Germany, too. Since the outbreak of the war in Ukraine, Rheinmetall has built new factories in Spain, Lithuania and Romania, growing into one of the largest munitions producers in the West.

Every new factory creates 500 to 1,000 new jobs directly, and several thousand more in the surrounding area, Mr. Papperger said.

And even though France has limited room to borrow to scale up its own spending, it, too, could benefit from higher military outlays in the rest of the region, Goldman Sachs economists say. It hosts the largest military in the European Union and is a major arms exporter.

Vicky Redwood, an economic adviser at Capital Economics, wrote in a March 13 analysis that in general, increasing military spending by 1 percent of G.D.P. would lift growth by around 0.5 percent. Outside of Germany, she wrote, a “reasonable” estimate is that European nations will raise their military spending by 0.5 to 1.5 percent as a share of output.

But several factors could affect how much military expenditure boosts growth, she wrote. Those include how much of the spending goes toward research and development and how efficiently the spending is done. Nothing is certain.

Apart from Rheinmetall, “the others are rather smaller players,” said Marcel Fratzscher, president of the German Institute for Economic Research. “I have doubts that this will be the future of Germany’s comparative advantage, changing from building cars to building tanks.”

Israeli ground forces pushed deeper into the Gaza Strip on Wednesday, taking over part of a major corridor that bisects the Palestinian enclave, in the most significant ground operation since the collapse of the cease-fire with Hamas.

The operation followed wide-scale Israeli aerial bombardment in Gaza that began early on Tuesday morning, ending the fragile truce that had held since mid-January. More than 400 people were killed in the airstrikes, according to the Gaza health ministry, which does not distinguish between civilians and combatants.

On Wednesday, the Israeli military said soldiers had begun “targeted ground activities” along the road — known as the Netzarim Corridor — to create a “partial buffer zone” between northern and southern Gaza. Israeli forces had widened their control “to the center of the Netzarim Corridor,” the military said.

Israel has not returned to full-scale war in Gaza that matches the intensity of its 15-month military campaign against Hamas. The Palestinian armed group has also not responded militarily to the Tuesday attack, which it said killed at least five members of its Gaza leadership.

It was unclear how many Israeli soldiers were now deployed along the part of the Netzarim Corridor or whether it marked the beginning of a sustained ground offensive. But Israeli leaders appeared to be gradually stepping up attacks, in an apparent effort to force Hamas to agree to more favorable terms for a settlement to free the dozens of hostages remaining in Gaza.

And unless Hamas capitulated, Israel was ready to continue ramping up pressure on the group, officials said.

Israel Katz, the Israeli defense minister, threatened Wednesday that Israel could again start ordering Palestinians to flee parts of Gaza that would become combat zones, as it frequently did before the cease-fire.

“What comes next will be much harder, and you will pay the full price,” Mr. Katz said in a video statement addressing Palestinians in Gaza.

But analysts said that it was far from clear that escalating Israeli military pressure could force Hamas to change its position in the cease-fire talks in the short term. Hamas has also vowed that Israel will not “achieve through war and destruction” what it failed to force the group to accept at the negotiating table.

Control of the Netzarim Corridor allowed the Israeli military to prevent hundreds of thousands of Palestinians displaced to the south from returning to their homes in northern Gaza. At least one major route along the coast still appeared to be outside of Israeli control as of Wednesday, allowing Palestinians to travel across the enclave.

During the war, Israeli soldiers fortified the road, building up a network of outposts and bases. They also leveled hundreds of buildings for miles around, giving them a clear line of sight, and funneled those allowed to cross through military checkpoints.

After the cease-fire with Hamas went into effect in January, Israel gradually withdrew from the Netzarim Corridor, although they remained deployed in a buffer zone inside Gaza and along the enclave’s border with Egypt. Palestinians returned home en masse in emotional scenes, often finding little but rubble where their homes and neighborhoods once stood.

Before the Israeli attack, mediators were seeking to broker an agreement between Israel and Hamas on the next steps in the cease-fire. Under the terms of the deal, the second phase is supposed to include an end to the war, the full withdrawal of Israeli forces and the release of the remaining living hostages in Gaza.

But neither side would accommodate the other’s demands. Israel was unwilling to end the war as long as Hamas remained in power in Gaza. Hamas refused to disband its armed battalions, send its leaders in Gaza into exile or release many more hostages unless Israel committed to permanently halting its campaign.

About 24 living Israeli and foreign hostages — as well as the remains of more than 30 others — are believed to still be held in Gaza, according to the Israeli government. Hamas and its allies abducted about 250 people during the Oct. 7, 2023 attack that ignited the war.

The first phase of the deal elapsed in early March. Almost immediately, Israel mostly shut off Gaza’s border crossings to humanitarian aid, preventing food, medicine and other supplies from entering the enclave. Later, the Israeli government cut off electricity it provided to a desalination plant in central Gaza.

Finally, on Tuesday, the Israeli surprise attack effectively shattered what remained of the fragile cease-fire. Israeli leaders said they could not allow the truce to continue without Hamas freeing additional hostages, while Hamas argued Israel was violating the agreement.

Israeli fighter jets bombarded sites across the Gaza Strip in an intense assault; the Israeli military said it was targeting Hamas operatives and sites. The pace of the bombing later slowed, although Israeli fighter jets continued striking across Gaza on Wednesday.

Miri Eisin, a retired Israeli colonel, said Israel was still escalating relatively slowly, given both the timing — the Muslim holy month of Ramadan — and hopes for an agreement to get more hostages out in the meantime.

“You couldn’t leave it in limbo — that would be Hamas defining the rules of the game,” said Ms. Eisin, a senior fellow at the International Institute for Counter-Terrorism, an Israel-based research organization.

But she added that Israel’s military actions thus far seemed unlikely to influence “the portions of Hamas who hold the hostages,” she said, referring to Hamas’s military leaders in Gaza.

Separately, the United Nations said one of its officers was killed and five others seriously injured in strikes on two compounds where they were staying in central Gaza. The Israeli military denied any connection to strikes on the compound. U.N. officials did not say who or what was behind the explosions.

“The locations of all U.N. premises are known to the parties to the conflict, who are bound by international law to protect them and maintain their absolute inviolability,” said Farhan Haq, the deputy spokesman for the U.N. secretary general.

Johnatan Reiss contributed reporting from Tel Aviv.

The leaders of the Democratic Republic of Congo and Rwanda have called for a cease-fire in eastern Congo in a bid to end the latest deadly chapter in a three-decade conflict.

The surprise announcement followed an unannounced meeting in Qatar on Tuesday, and analysts said it could either signal a de-escalation in a conflict that has threatened to become a regional war, or be the latest failed attempt to bring peace to this part of Central Africa.

Presidents Félix Tshisekedi of Congo and Paul Kagame of Rwanda committed to an “immediate and unconditional cease-fire,” according to a joint statement issued with Qatar, though they did not say how the cease-fire would be carried out or monitored.

The meeting was the leaders’ most significant step since a Rwanda-backed armed group, called M23, captured eastern Congo’s two largest cities and large sections of the territory in an offensive that began in January.

“This is the first time a concrete statement is coming from both leaders,” said Oluwole Ojewale, a scholar with the Institute for Security Studies who focuses on Central Africa.

The fighting has displaced more than 700,000 people since January, according to the United Nations refugee agency, and killed thousands of others.

The leaders’ meeting came a day after the European Union announced sanctions on the Rwandan government and military officials over the backing of M23. Rwanda retaliated by severing diplomatic ties with Belgium, a country that was once the colonial ruler in both Congo and Rwanda and which has been a leading voice for sanctions on Rwanda over its involvement in the conflict.

Mr. Tshisekedi and Mr. Kagame said in the statement that they wanted to “establish solid foundations for lasting peace” in eastern Congo, where three decades of fighting over ethnic tensions and access to land have killed millions of people.

Previous attempts at truces have failed, either because cease-fires have been violated or because the warring parties backed out of talks at the last minute — including a meeting that had been scheduled for Tuesday between Congo’s government and M23’s leadership.

M23 said on Monday that it would not participate in that gathering, which was set to be held in Angola, whose president is seen as more amenable to Congo’s cause. Instead, Rwanda’s and Congo’s presidents met in Qatar, which is a close ally of Rwanda.

“Congo might have realized that it had to make a concession,” said Jason Stearns, the co-founder of the New York University-based Congo Research Group.

M23, a group created in 2012, is armed and commanded by Rwanda’s army, according to the United Nations, the United States and the European Union. Rwanda denies backing the group and says that the violence in neighboring Congo is threatening its security.

The group, which according to U.N. estimates has 6,000 to 9,000 soldiers, now controls a Congolese area the size of Louisiana that is rich in gold and other minerals, like coltan. That area includes Goma and Bukavu, two key hubs on the border with Rwanda.

It is unclear whether M23, which has denied any affiliation with Rwanda’s government, will heed the calls for a cease-fire. In the past, the group has declared unilateral cease-fires, only to violate them days later, including after its capture of Goma.

A spokesman for the group did not respond to a request for comment on Wednesday.

Neither Congo’s weak army nor international pressure, including a unanimous condemnation from the U.N. Security Council, has been able to stop M23’s advance. Rwanda’s government has held strong in its position despite Western nations’ suspension of development aid and some export activities because of its role in the conflict.

Mr. Ojewale said that the United States could have been in a position to convene peace talks, but given that it was not a priority for the Trump administration, Qatar stepped in. Previous attempts by President Emmanuel Macron of France have also failed.

“It appears now that the countries that actually have the leverage to bring warring African leaders to the table are countries like Turkey, Saudi Arabia, the U.A.E. — who are completely outside the shores of the continent,” Mr. Ojewale said.

Experts say that a few options are now on the table, though none appear imminent. They include peace negotiations in Congo that could lead to a power-sharing agreement and more autonomy for eastern Congo, which is 1,000 miles from the capital, Kinshasa; the integration of M23 fighters into the Congolese Army; the establishment of a buffer zone; or even Rwandan annexation of the region.

“Rwanda is in a bad place in terms of international pressure, but on the ground they’re not,” said Mr. Stearns. “This ‘no peace, no war’ situation could last for quite some time, and it’s not unfavorable to Rwanda.”

For nearly 60 days, Gazans did not have to tally the newly dead as a fragile truce between Israel and Hamas held. Hostages and prisoners were freed, food and supplies returned to markets, and people picked their way through ruins they had called home.

On Tuesday, after weeks of fruitless talks to extend the cease-fire, Israeli warplanes bombarded cities up and down the Gaza Strip, and the counting began again.

More than 400 people were killed in the strikes, according to Gaza’s health ministry, whose figures do not distinguish between civilians and combatants. Among the dead were 130 children, the U.N. Children’s Fund said, reporting that some of the airstrikes hit shelters where families were sleeping.

After weeks of relative calm, the attacks on Tuesday appeared to catch many Gazans off guard, including those who had returned to battered neighborhoods and were sheltering in close quarters together. The result was one of the deadliest single-day tolls of the entire war, which began with the 2023 Hamas-led attack on Israel in which about 1,200 people were killed and 250 abducted.

The Israeli military response devastated Gaza, killing tens of thousands of people, displacing millions and flattening towns. Day after day, month after month, survivors searched for the wounded and the dead.

They were doing so again in the hours after Israel’s latest airstrikes, which began before dawn on Tuesday.

The office of Benjamin Netanyahu, the Israeli prime minister, said that he had ordered the strikes after Hamas’s “repeated refusal” to release the 59 hostages still being held in Gaza. Fewer than half are believed to be alive.

In an address, Mr. Netanyahu suggested that Israel would keep launching strikes in tandem with negotiations with Hamas. “This is just the beginning,” he said.

After the strikes, some went to morgues to identify missing relatives. Others wrapped bodies in shrouds and hurried to bury them. During much of the war, traditions of death like funeral processions and mourning tents had themselves become too dangerous to perform.

Many of the dead have been buried in common graves, courtyards and backyards, with prayers said quickly and under cover, rather than under the open sky.

With only a few of Gaza’s hospitals still functioning, survivors tried to administer whatever treatment to the wounded they could.

The dead and injured include a huge number of children, aid workers say. And while some grievously wounded children have left Gaza for medical care abroad, the border crossings are now closed. Those wounded in this week’s attacks can seek help only within the territory’s bounds.

More than 48,000 people have been killed in Gaza since the war began, according to local officials. Palestinians have mourned in the places they can, often outside hospitals or by the wreckage of their homes.

The Israeli military said on Tuesday that it had struck sites and individuals affiliated with Hamas and another militant group, Palestinian Islamic Jihad, across the enclave.

Hamas quickly re-emerged in public after the cease-fire was reached, seeking to show its dominance over Gaza and staging elaborate hostage release ceremonies that infuriated Israelis. In addition to Mr. Netanyahu’s assertion about Hamas’s refusal to release hostages, the Israeli military said it struck Gaza to prevent planned attacks on Israelis.

In past strikes on shelters, Israel has said that militants used them as bases and that it tries to minimize the harm to civilians. On Tuesday, the military hit at least one tent housing displaced people in Khan Younis, a city in southern Gazan where thousands had fled.

The first phase of the cease-fire ended on March 1, and although neither Israel nor Hamas immediately resumed fighting, the Israeli government began ratcheting up its pressure on Gazans.

It halted all aid into the territory and severed sources of electricity, forcing Gazans to scavenge for cooking firewood from the remains of homes.

Food and fuel are once again scarce. Scalpers are selling bread for three times the original price, and there is no more gasoline arriving for generators, ambulances or anything else.

The Israeli military has issued new evacuation orders, warning Palestinians about neighborhoods subject to strikes. Families heeding them packed up again on Tuesday, taking whatever they could.

With donkeys pulling carts, Palestinians who had returned only weeks ago to Beit Hanoun, in northern Gaza, left again. Israel ordered evacuations in the area on Wednesday, warning residents of what it called “combat areas.”

Israel advanced deeper into Gaza on Wednesday, saying its soldiers had seized parts of a major corridor separating the enclave’s northern half from the south. The military said its goal was to create a “partial buffer zone” there.

Some wells are still functioning in central Gaza, but they supply only brackish water, which could cause long-term health problems, aid workers warn. Israel’s energy minister has suggested that water could soon be cut off. Its Foreign Ministry maintains that the territory has received sufficient aid and that Hamas is exploiting shipments.

Gaza has had little electricity since the first days of the war, when Israel cut off sources in its initial response to the 2023 Hamas attack. For months, Gazans lived in blackout conditions, with the territory’s essential services relying on solar panels and generators.

After another round of attacks, the panels have become more valuable than ever.

But solar panels can do only so much. Many Gazans remain in darkness.

Follow our live coverage of the Trump administration and Ukraine cease-fire talks.

When the Kremlin released its summary of President Vladimir V. Putin’s call Tuesday with President Trump, one thing was unmistakable: The Russian leader hadn’t retreated from his maximalist aims in Ukraine and so far has conceded little.

Much of what Mr. Putin agreed to during the call — including a limited 30-day halt on energy infrastructure strikes by both sides, a prisoner exchange and talks about security in the Black Sea — was spun as a concession to Mr. Trump in the respective summaries of the conversation released by Moscow and Washington.

But all were goals that the Kremlin has pursued and seen as advantageous in the past. Russia and Ukraine previously reached a tacit mutual agreement to refrain from energy infrastructure strikes, which have caused pain for both Moscow and Kyiv. Russia has long conducted prisoner exchanges with Ukraine, seeing the repatriation of its soldiers as a key Kremlin interest. And uninterrupted trading in the Black Sea is critical to Russia’s economy.

The lack of clear concessions on the Russian side stoked fears among Ukraine’s backers that Mr. Putin was playing for time, hewing to his staunch demands while hoping, in the meantime, that Washington’s tattered relationship with Kyiv fully breaks or that Ukrainian forces face a battlefield collapse.

Mr. Putin’s demands on Ukraine appeared unchanged. During the call, according to the Kremlin, Mr. Putin reiterated requirements for a comprehensive 30-day cease-fire that he knows are nonstarters for Ukraine. According to the Kremlin, he claimed that the Ukrainians had sabotaged and violated agreements in the past, and accused Ukraine of committing “barbaric terrorist crimes” in the Kursk region of Russia.

By Wednesday, the Kremlin was already accusing Kyiv of violating the limited cease-fire on energy infrastructure, even though President Volodymyr Zelensky of Ukraine had yet to be briefed by Washington on the call or formally comply with the deal. Later in the day, Mr. Zelensky did agree in a phone call with Mr. Trump to accept Russia’s offer for a mutual pause in attacks on energy targets as a step toward a fuller cease-fire, according to the Ukrainian leader and Trump administration officials.

During Tuesday’s call, the Kremlin said, Mr. Putin also identified his “key condition” for settling the conflict more broadly: a complete cessation of outside military and intelligence support for Kyiv. Such an outcome, analysts say, would make Ukraine, a country far smaller than Russia, permanently hostage to Moscow’s overwhelming military superiority and forever stranded within the Kremlin’s orbit, without any counterbalancing backers.

Mr. Trump, in an interview with Fox News, denied that Mr. Putin set out the cessation of military and intelligence aid to Ukraine as a condition to resolving the conflict.

“We didn’t talk about aid, actually, we didn’t talk about aid at all,” Mr. Trump told the interviewer, Laura Ingraham, contradicting the Kremlin’s summary of the call.

The Kremlin may be hoping that during the course of negotiations, an already impatient Washington walks away from Ukraine for good, freeing Mr. Putin to continue his war while also separately re-establishing relations with the United States. Russia may also be counting on the possibility that Kyiv, facing an increasingly dire picture on the battlefield and the loss of its biggest backer, ultimately agrees to an erosion of its sovereignty that benefits the Kremlin.

“The best outcome for Putin is one where he accomplishes his aims in Ukraine and can normalize relations with the U.S.,” said Andrea Kendall-Taylor, a former U.S. intelligence official who is now an analyst at the Center for a New American Security, a think tank in Washington. “So Putin wants to string Trump along to give him just enough to see if he can accomplish that.”

Ms. Kendall-Taylor added that Mr. Putin will feel he has little to lose, believing that Mr. Trump, who has made no secret of his dim view of Ukraine and of Washington’s European allies, “won’t be willing to really ramp up pressure on Russia or recommit to Europe.”

“There is a lot of incentive for the Russians to participate, to play along and look for every opportunity to use this construct to their maximum advantage,” Ms. Kendall-Taylor said.

Mr. Putin also has significant advantages on the battlefield. His forces are winning back territory. Ukraine’s biggest and most important supporter, the United States, is openly itching to abandon Kyiv, as well as Europe more broadly. Europe, suddenly realizing its peril without U.S. backing, has been caught flat-footed and is now scrambling to figure out how to secure its own defense — let alone that of Ukraine.

“In Russian diplomatic functioning, negotiations often are just tools of winning time and depriving the adversary of its balance,” said Andras Racz, a senior research fellow at the German Council on Foreign Relations.

Mr. Racz said that Washington’s stated desire to reach a quick resolution to the conflict confers a certain advantage to Moscow, which is “not in a hurry.”

He held out the possibility that the Trump administration, faced with Mr. Putin’s refusal to cede ground on Ukraine, could begin applying pressure on Russia. Mr. Trump has made such threats in the past.

The White House could also offer Mr. Putin more.

After the breakup of the Soviet Union, Washington’s power in Europe grew significantly, with many of the countries that once answered to Moscow joining NATO and ultimately the West. Mr. Putin has never accepted that outcome, making him eager to hold broader discussions on European security with the Trump administration. His apparent hope is that Washington will not only agree to an arrangement that places Ukraine in Russia’s orbit but also will concede a broader curtailment of U.S. influence on the continent. Washington’s ability to grant those broader wishes gives the White House some measure of leverage, even if previous administrations ruled them out as impossible.

“Trump has few options to counter either a Russian rejection or protracted feigned compliance,” wrote Alexander Baunov, a Russian author and political analyst. “The most effective method will be the carrot rather than the stick: the temptation of a major deal.”

Russia, while giving little on Ukraine, has begun trying to lure Washington with the fruits of a rapprochement. Russian officials have been touting their vast reserves of rare earth metals, saying they would be happy to exploit them with American companies, and holding out possible deals for American investors in the Russian energy sector.

Mr. Putin and Mr. Trump spent part of the discussion on Tuesday talking about what the Kremlin called “a wide range of areas in which our countries could establish interaction,” including ideas about cooperation in the energy sector. The Russian leader, according to the Kremlin, secured Mr. Trump’s agreement to hold hockey tournaments with Russian and American professional players facing off against one another.

Alexander Gabuev, director of the Carnegie Russia Eurasia Center, said that the Kremlin would be hoping to get the United States to restore ties without predicating renewed relations on an end to the fighting in Ukraine. That’s why, he added, the Kremlin is front-loading the discussion with all the potential benefits for the United States from a renewed relationship with Russia.

“The impression is that they have a very, very, very good reading of Trump,” Mr. Gabuev said of the Kremlin. “They know where the weak spots are, they know how to massage his ego. To me, the Russian team is winning at this point.”

Follow our live coverage of the Trump administration and Ukraine cease-fire talks.

Russia and Ukraine have agreed to a limited cease-fire to stop attacks on energy infrastructure, the first significant step toward de-escalation since the start of the full-scale war more than three years ago.

It was not immediately clear how and when the partial cease-fire would take hold. On Wednesday, Ukraine and Russia traded accusations of attacks against each other’s energy infrastructure, highlighting the lack of trust between the two countries and how tenuous any deal will be.

Strikes against energy facilities have been a key part of each country’s efforts to weaken the other. Russia has launched repeated attacks on Ukraine’s power grid to undermine its war effort by making life as difficult as possible for civilians, experts say. Ukraine’s strikes on Russian facilities are aimed at cutting the revenues of Russia’s sprawling oil industry, which have been used to fund the country’s military.

The Strategy Behind the Attacks

Russia began attacking Ukraine’s energy infrastructure in October 2022 after it became clear that its initial plan to achieve a swift victory had failed. Moscow opted for a war of attrition in which Ukraine’s energy infrastructure became a key target.

Ukraine began repeatedly targeting Russia’s energy infrastructure in early 2024 to try to inflict pain on the heart of the Russian economy — its oil and gas industry — and to limit the supply of fuel to its military. Kyiv’s aim appeared to be twofold, experts say: to reduce Russia’s oil revenues, and to produce a psychological effect by causing large-scale fires at critical infrastructure facilities.

Russian attacks on Ukraine’s energy infrastructure have been a key part of Moscow’s effort to bring the country to its knees. The goal, energy experts say, has been to choke off the energy resources that fuel Ukraine’s economy and ultimately its war effort. But it also appears intended to make life so unbearable for people — plunging them into cold and darkness — that it breaks their morale.

Volodymyr Kudrytskyi, the former head of Ukrenergo, Ukraine’s national electricity operator, said Russia constantly changed its targets and tactics to undermine Ukraine’s ability to defend its energy system.

Moscow has used complex waves of long-range drones and ballistic missiles to overwhelm Kyiv’s air defenses. After Ukraine began reinforcing its main electricity substations with concrete bunkers, Russia shifted to striking thermal power plants directly and to attacking less protected substations connected to nuclear power plants.

The Effect on Russia

Over the past year, Ukrainian drones have flown deep into Russian territory, hitting oil refineries, depots, storage units, pipelines and pumping stations. The attacks have disrupted oil flows that pass through Russian seaport oil terminals and the Druzhba pipeline, which takes crude to some European countries.

That has threatened to undercut Moscow’s revenue from energy sales abroad. It has not been possible to independently determine how much of Russia’s oil revenues have been affected by the attacks.

The attacks on oil refineries reduced the country’s refining capacity by around 10 percent at one point, according to Reuters, which has been calculating the effect of damage.

But Russian oil giants have also been able to quickly repair some damage. According to Mikhail Krutikhin, an independent Russian energy analyst living in exile in Oslo, the damage inflicted on Russian oil refineries “has never been critical.”

Mr. Krutikhin said in a phone interview that Russia could always redirect crude oil flows away from a damaged refinery since the country has so many refineries. Sometimes, refineries had to start producing jet fuel that had more sulfur in it, he said.

“This is bad for the environment, but fighter jets can continue to fly,” Mr. Krutikhin said. He added, however, that the attacks could produce damage in the long term, because some parts of oil refineries might take years to get produced and installed.

Sergey Vakulenko, an energy expert at the Carnegie Endowment for International Peace, a research group, said Russian oil companies had to spend no more than $1 billion to repair the damage inflicted by Ukrainian attacks.

The Effect on Ukraine

Since the fall of 2022, Moscow has repeatedly used drones and missiles to strike substations that distribute electricity, power plants that generate it, and, more recently, gas facilities.

The Kyiv School of Economics estimates that damage to Ukraine’s energy sector has reached at least $14.6 billion. Several hydroelectric and thermal power plants have been completely destroyed by the attacks.

By the end of last year, Ukraine’s total electricity-generating capacity had dropped to some 22 gigawatts, less than half of its prewar level, according to DiXi Group, a Ukrainian energy research organization.

The power shortages have forced Ukraine to impose nationwide rolling blackouts to ease strain on the grid. On some days, neighborhoods in Kyiv, the capital, had as little as four hours of electricity. Many civilians have resorted to candles to light homes and relied on cellphone flashlights to navigate unlit streets.

Water pumping systems have sometimes failed, making life difficult for citizens as the flow of running water to their homes was cut. During the first winter of the war, long lines formed at wells in Kyiv as residents hauled jugs of water back to their unheated apartments.

Still, Russia has failed in its attempts to completely collapse Ukraine’s energy system. Ukraine has endured the assaults, thanks to Western-supplied air defenses that enabled it to gradually intercept more Russian missiles, round-the-clock work by engineers to repair vital equipment and the energy-saving ingenuity of residents.

Ukraine has also relied on its three operational nuclear power stations, which Russia has avoided targeting to prevent a nuclear disaster, to meet up to half of the country’s electricity needs during certain periods.

Who Has More to Gain?

Experts say it is difficult to determine which country stands to gain more from a cease-fire on attacks targeting energy infrastructure.

Mr. Kudrytskyi said a pause would give Ukraine crucial time to repair substations and power plants without the threat of new strikes.

The cease-fire would also give Ukraine time to replenish its stocks of critical spare equipment, including valuable transformers needed to transmit electricity from power stations to people’s homes. Ukraine has burned through its stocks in an effort to replace damaged equipment.

For the Kremlin, the suspension in Ukrainian attacks would mean that the war and its effects would appear even more distant to the Russian public. Moscow also would no longer need to worry that such attacks could damage critical oil infrastructure.

Turkey arrested the top political rival of President Recep Tayyip Erdogan on accusations of corruption and terrorism on Wednesday, days before he was set to be named the opposition’s candidate in the next presidential election.

The opposition blasted the arrest of the rival, Mayor Ekrem Imamoglu of Istanbul, as politically motivated and said that the government was trying to remove a potential political threat to Mr. Erdogan.

Mr. Imamoglu, 54, accused Mr. Erdogan, his associates and state prosecutors of orchestrating his arrest.

“This immoral and tyrannical approach will undoubtedly be overturned by the will and resilience of our people,” he said in a voice message sent when the police were at his home to arrest him and shared by his aides.

In a video shared on social media, also before his arrest, Mr. Imamoglu spoke from inside his closet as he knotted his tie and said that the government was “usurping the will of the people.”

“We are facing great tyranny,” he said. “But I want you to know that I will not be discouraged.”

Critics have long accused Mr. Erdogan, who became prime minister in 2003 and president in 2014, of using state institutions, including the courts and the security services, to undermine his political rivals. Mr. Erdogan’s defenders cite his history of electoral victories as proof of his popularity.

Mr. Imamoglu had on three occasions since 2019 beaten candidates chosen by Mr. Erdogan to run Istanbul, Turkey’s largest city and economic powerhouse. And Turkey’s main opposition party was expected to formally nominate him as its presidential candidate during a primary on Sunday.

The head of the main opposition party, Ozgur Ozel, called on party members to go ahead with the scheduled primary vote.

“We are faced with a coup attempt against our next president,” Mr. Ozel wrote on social media.

In Brussels, the president of the European Commission, Ursula von der Leyen, called the arrest “deeply concerning.”

“Turkey must uphold the democratic values, especially the rights of elected officials,” she told reporters.

Foreign Minister Annalena Baerbock of Germany said the arrests showed that “the space for opposition politicians is getting smaller and smaller.”

The arrests have also rattled investors at a time when the government is struggling to tame persistently high inflation that has hurt Turkish families. The country’s stock market fell so swiftly that trading was halted twice. The national currency fell about 12 percent to an all-time low of 42 Turkish lira to the dollar before recovering some of its losses.

Turkey’s next presidential election is scheduled for 2028, but Parliament is widely expected to call for early elections before then.

Mr. Erdogan is in the second of the two terms he is allowed by the Constitution. But an early election would allow him to run again, on the grounds that he did not complete his second term. Many in the opposition also want an early vote because they believe that chronic inflation, which has been exacerbated by Mr. Erdogan’s policies, will help them at the polls.

Mr. Erdogan, 71, and officials in his ruling Justice and Development Party have not publicly discussed who their candidate will be. But Mr. Erdogan has been Turkey’s predominate politician for more than two decades, and he has no clear successor. So he is widely expected to run.

Sinem Adar, a Turkey expert at the German Institute for International and Security Affairs, said the government had been laying the groundwork to exclude Mr. Imamoglu from the race for some time, given the challenge he would pose to Mr. Erdogan and the ruling party’s poor showing in local elections last year.

“There is a lot of discontent in the population,” she said.

But the prevailing international mood, including the rise of far-right parties in Europe and the Trump administration’s nationalist focus, could make it easier for Mr. Erdogan to act against his rivals.

“The international context and the geopolitics help Erdogan double down on the dissidents, on the opposition,” Ms. Adar said.

The Congress of Local and Regional Authorities of the Council of Europe, which promotes local democracy on the continent, condemned the arrest, saying that it appeared aimed at exerting “pressure on a political figure considered as one of the main candidates in forthcoming presidential elections.”

Police arrested Mr. Imamoglu just after dawn at his house. Prosecutors said that related arrest warrants had been issued for more than 100 people, and police also detained two Istanbul district mayors and a number of Mr. Imamoglu’s senior aides.

The Istanbul prosecutor’s office said that Mr. Imamoglu was accused of leading a criminal organization. Prosecutors say he took part in corrupt practices in municipal business and accused him of engaging in bribery, fraud, money laundering, personal enrichment and bid rigging. A Turkish court also ordered the seizure of a construction company co-owned by Mr. Imamoglu, the prosecutor’s office said.

He also faces accusations of aiding a terrorist organization linked to his coordination with a pro-Kurdish political party during last year’s municipal elections, prosecutors said. Mr. Imamoglu won that election handily against a candidate backed by Mr. Erdogan.

Mr. Imamoglu has yet to be indicted on specific charges related to these accusations, but he could be kept in detention while prosecutors pursue their investigation.

The office of Istanbul’s governor, who is appointed by Mr. Erdogan, took steps on Wednesday to head off protests about the arrests.

Public demonstrations have been banned in the city for four days and two subway stations were closed, including in Taksim Square, a central transportation hub and large plaza where rallies have often been held.

Turkey also restricted access to social media platforms including X, YouTube, TikTok and Instagram, according to NetBlocks, an internet monitor.

By nightfall, thousands of protesters had gathered outside City Hall and other, smaller protests were being held elsewhere in Istanbul; in the capital, Ankara; and in other cities.

Mr. Imamoglu’s arrest follows numerous court cases and other procedural moves against him that the opposition says are aimed at eliminating him as a political force.

In recent years, he has faced charges of corruption during his previous role as an Istanbul district mayor, and he is appealing a 2022 conviction on charges of insulting judges on the Supreme Electoral Council, which oversees elections.

Some of the cases against him could result in his being temporarily barred from politics, meaning that he could be ousted as mayor and prohibited from running for president.

In another move that Mr. Imamoglu’s supporters say seeks to exclude him from the presidential race, his alma mater, Istanbul University, announced on Tuesday that it had annulled his diploma, citing improper procedures in his transfer in 1990 from a university in Turkish-controlled Northern Cyprus.

The Turkish Constitution stipulates that the president must be a university graduate.

Mr. Imamoglu has argued that there was nothing improper about his transfer and that a previous government inquiry into the matter had found nothing amiss.

Last month, the Istanbul prosecutor’s office requested a new inquiry, which led to the cancellation, a decision that Mr. Imamoglu is expected to appeal.