While Israeli airstrikes continued in other parts of Gaza, Israel agreed to pauses in the fighting in specific areas to allow the vaccination drive to proceed, and “until now they work,” Dr. Peeperkorn said.

Health teams will next take the effort to southern Gaza, where the W.H.O. estimates that it needs to reach 340,000 children before going to the north to inoculate some 150,000 more.

The W.H.O. and its partner agencies in Gaza say they need to reach 90 percent of children under 10 to avert the spread of polio. Gazans are experiencing an explosion of infectious diseases in the overcrowded and unsanitary conditions created by the war and the destruction of Gaza’s health care infrastructure.

Medical Aid for Palestinians, an aid group supporting the effort, said in a statement on Tuesday that the main challenges of the campaign included ensuring safe access for medical workers and keeping the vaccines refrigerated in the face of electricity outages and fuel shortages, as well as the consequences of damage to sanitation and health care infrastructure.

The success of the vaccination campaign relies heavily on the staggered pauses in fighting in different regions of the Gaza Strip, which both Hamas and Israel agreed to and which they appear to be respecting. The pauses are intended to allow families and aid workers to safely reach vaccination sites between the hours of 7:30 a.m. and 2 p.m.

Mohammed Abu Hajar, a 41-year-old driver who has been sheltering in central Gaza, where the campaign kicked off, said he took his two children to get vaccinated because “a child getting sick could lead to death,” given the collapsed health care system and a severe lack of medical supplies. “There is no other option,” he said.

But the vaccination campaign brought with it another blessing for Mr. Abu Hajar: the temporary pause in fighting, during which he said he had been able to “move around comfortably and feel some reassurance” that there would not be strikes.

Mazen Abdulwaha, a displaced father of seven, said he had been worried about his children ever since he first heard that the virus had been detected in Gaza’s wastewater, because they “live in camps where wastewater follows us everywhere.” He took his three youngest children to get vaccinated as soon as the campaign began.

Like others in central Gaza, Mr. Abdulwaha, 36, said his family was “trying to take advantage” of the pauses in fighting during the four days of the campaign in that area, but he remained cautious because he did not trust Israeli forces to adhere to them. “We had to bear this risk to vaccinate our children and protect them from diseases,” he said.

But for some, the humanitarian pauses offered little relief after more than 10 months of a brutal war.

“A calm of five to six hours means nothing,” said Mohammed al-Sapti, a 32-year-old who is sheltering in Nuseirat in central Gaza. “There is no such thing as temporary safety as long as we are living under siege, exhaustion and torture,” he added.

Iyad Abuheweila contributed reporting from Istanbul, and Ameera Harouda from Doha, Qatar.

Israeli soldiers withdrew from Tulkarm last week after two days of fighting, even as a raid continued in the city of Jenin to the north. But on Monday evening, Israeli forces began again deploying throughout Tulkarm in large numbers, said Ma’mun Abu al-Heija, a resident of Nur Shams, a neighborhood on the city’s outskirts.

On Tuesday, a 16-year-old Palestinian girl was killed by Israeli gunfire in Kafr Dan, just outside Jenin, the Palestinian Ministry of Health in Ramallah said in a statement. The circumstances were not immediately clear and the Israeli military did not respond to a request for comment.

Israeli troops typically use less force in operations in the West Bank than they do in Gaza, much of which has been destroyed in Israel’s nearly 11-month-long war against Hamas. But these raids have been unusually destructive, residents and Palestinian officials in the West Bank said.

Israeli bulldozers have torn up main roads — in what military officials say is an effort to unearth improvised explosives planted by militants — along with water pipes and electrical cables. Many Palestinians in Jenin have spent days without electricity or running water, according to the local governor, Kamal Abu al-Rub.

Some residents of Jenin have begun to flee, fearing for their lives. Omar Obeid, 62, said he had left the city over the weekend with his children and many of his neighbors, walking through streets torn up by Israeli forces. They had been trapped at home for days without running water or electricity, he said.

“We tried to take a path that would avoid the army, but we still were risking our lives,” he said in a phone interview.

Eventually, he said, they reached a relative’s home in nearby Yabad and took shelter. Intermittent gunfire and explosions are distant but still audible, he said.

Israeli officials have described the raids as necessary to combat rising Palestinian militancy, particularly a spate of attempted bombings, over the past few weeks. The return of the tactic has revived difficult memories for Israelis, whose national psyche was scarred by dozens of Palestinian suicide attacks in the early 2000s that left hundreds of civilians dead.

Over the weekend, two cars rigged with explosives burst into flames during attacks in the southern West Bank. Israeli forces killed the two assailants, who Hamas said were members of its armed wing. And on Monday, Israel’s police said sappers had disarmed a car bomb near the Israeli settlement of Ateret in the central West Bank.

In mid-August, Hamas and its ally Palestinian Islamic Jihad claimed responsibility for a bombing in Tel Aviv that wounded one person and killed the assailant. The armed groups claimed it was a suicide bombing.

How many hostages are still in Gaza?

More than 60 living hostages, and the bodies of about 35 others taken captive on Oct. 7 but believed to be dead, are still in Gaza, according to the Israeli authorities.

In all, about 250 people were abducted on Oct. 7, according to Israeli officials, who include in that number 37 people who were murdered in the initial attack and whose bodies were taken back to Gaza. Those taken were mainly civilians but also included military and security personnel. They were men, women and children, Israeli citizens as well as people who were citizens of the United States, Britain, France, Russia, Germany, Mexico, Thailand and other countries.

How many hostages are Americans?

In all, 12 people with U.S. citizenship were abducted to Gaza on Oct. 7, according to the Israeli government. Two of them, Judith Raanan and her daughter, Natalie Raanan, were freed on Oct. 20 after pressure on Hamas by the United States and Qatar. Two others were released during a cease-fire in November.

One of the hostages, Hersh Goldberg-Polin, 23, a dual Israeli American citizen, was among the six who were found dead in Gaza over the weekend. He had been taken from a music festival in southern Israel on Oct. 7.

The American Jewish Committee, an advocacy organization for Jewish people around the world, on Saturday listed four American citizens who were still being held alive in Gaza. They are Edan Alexander, 20; Sagui Dekel-Chen, 35; Omer Neutra, 22; and Keith Siegel, 64. Three others are presumed dead: Itay Chen, 19; Gadi Haggai, 73; and Judi Weinstein Haggai, 70.

How many hostages have been freed?

Since Oct. 7, 117 people have been released, according to the Israeli authorities. More than 100 were freed during a one-week cease-fire at the end of November in exchange for 240 Palestinians held in Israeli detention.

In addition, eight people have been freed during Israeli military operations. Last week, a Bedouin Arab citizen of Israel was rescued after Israeli commandos found him alone in a tunnel in southern Gaza.

In the most high-profile hostage rescue, in June, soldiers and special operations police rescued four hostages from buildings in the town of Nuseirat, in central Gaza. Scores of Palestinians, including women and children, were killed during that operation, according to the health ministry in Gaza.

In December, Israeli forces mistakenly killed three hostages who had escaped from their captors and were attempting to approach them. The army said the shooting violated its rules of engagement.

What are the conditions like for those still in captivity?

Hostages who have returned from captivity in Gaza have shed some light on where they were held and what the conditions were like. Some were held in hospitals, others in apartments, a mosque and even a destroyed supermarket. Hamas has also been known to hold hostages underground in a network of tunnels. The Israeli military said on Sunday that the bodies of the six slain hostages were found in a tunnel.

Many hostages who have left Gaza have described being moved repeatedly during their captivity, under heavily armed guard. They reported being subjected to physical and psychological abuse.

Andrey Kozlov, 27, a Russian Israeli, provided a detailed account of his time in captivity after he was rescued by the Israeli military in June. He described being held in six locations in the first two months and being moved to an apartment in mid-December. In some places, he and the hostages he was held with had only a pail for a toilet, and food was scarce.

After the rescue of Mr. Kozlov and three other captives, Dr. Itai Pessach, the head of a medical team for returning hostages, said they were malnourished. “They were all abused, punished and tortured physically and psychologically in many ways,” he said.

Gabby Sobelman contributed reporting.

Ballistic missiles can travel faster than the speed of sound and reach a target anywhere in Ukraine in a matter of minutes, which gives little to no time for air raid warnings to sound and help people get to safety. Ukraine’s Defense Ministry said the gap between the sounding of warning sirens and the strike in Poltava was so short on Tuesday that many people were killed on their way to shelter.

Ukraine has begged since the outset of Russia’s full-scale invasion in February 2022 for more tools to close its sky to Russian missiles. But the first Patriot missile systems from the United States and Germany — the only proven defense against ballistic missiles — did not arrive until the spring of 2023.

The Patriot was originally designed to hit aircraft but was re-engineered after the Gulf War to be primarily used to strike tactical ballistic missiles, as those weapons grew in prevalence and importance on the battlefield. It is one of the scarcest weapons systems in the U.S. arsenal, in part because they are in demand around the globe and because they are expensive and take a long time to produce.

Mr. Zelensky of Ukraine has said he desperately needs at least seven Patriot batteries to fend off attacks across the country. Germany has sent three and, in July, President Biden announced the deployment of a second Patriot missile system from the United States. Other American allies also have Patriots: Romania has pledged one, and the Netherlands has given parts of the complex system. U.S. officials have said they hope European powers will send more.

It was unclear if Ukraine used any of those Patriot batteries to try to fend off Tuesday’s attack in Poltava, the scale of which added fresh urgency to Ukrainian pleas for more defenses against ballistic missiles. Ukraine’s air force said the missiles had arrived “a matter of minutes” after they were launched.

“Ballistics are extremely dangerous, especially for the frontline areas,” the air force said in a statement to Ukrainian media.

At the same time, Ukrainian officials have urged allies to allow the use of long-range weapons provided by the West, such as rockets and cruise missiles, to strike back at targets inside Russia — a call Mr. Zelensky took up again on Tuesday.

“Long-range strikes that can protect us from Russian terror are needed now, not later,” he said on social media. “Every day of delay, unfortunately, means more lost lives.”

Marc Santora, Maria Varenikova and Lara Jakes contributed reporting.

President Volodymyr Zelensky of Ukraine said that it was one of the largest attacks since Russia’s full-scale invasion began 30 months ago. The strikes knocked out power in some cities, including the capital, continuing a pattern of attacks on the country’s energy infrastructure.

Early the next morning, Russia launched another barrage, and one missile hit a hotel in the central Ukrainian city of Kryvyi Rih, killing four people. There was also a smaller round of strikes on Wednesday.

Moscow, which has been conducting aerial assaults on Ukraine every few weeks, gave no reason for the timing of the strikes, but it came weeks after Ukraine launched a surprise incursion into the southern Russian region of Kursk. President Vladimir V. Putin of Russia had vowed a decisive response.

Russia continued to pound urban areas close to the front lines throughout the week. On Wednesday, a Russian attack killed four members of a family in the tiny community of Izmailivka in the Donetsk region, the state prosecutor said. The settlement is a few miles west of Russian lines and close to the city of Pokrovsk, which Moscow is trying to capture.

Most of the missiles and drones were shot down by Ukraine’s air defense systems, the Air Force said. F-16 fighter jets, recently delivered by the country’s allies in NATO, were deployed in that effort, intercepting and shooting down three cruise missiles and a drone.

But on Thursday, the head of Ukraine’s air force, Lt. Gen. Mykola Oleshchuk, announced that one of the jets had crashed in combat during the operation on Monday and its pilot had been killed. He said that the crash, which came as a shock to many Ukrainians so soon after the deployment of the coveted fighter jets, was being investigated.

The following day, Mr. Zelensky announced that Lt. Gen. Oleshchuk had been fired.

Russian fire was also directed at Ukraine’s second largest city, Kharkiv, which is situated within range of Russian artillery and has been repeatedly assaulted since the start of the full scale war.

On Friday, a Russian glide bomb hit a children’s park and a mid-rise apartment block in the city, killing seven people and wounding nearly 60 others, according to the head of the regional military administration, Oleh Syniehubov.

Two days later, Russian forces bombarded residential areas of the city, wounding more than 40 civilians, Ukrainian officials said. At least 10 explosions had rocked the city.

The attack on Tuesday extended a wave of assaults on cities across Ukraine that Russia began a week ago, even as it pushes forward with fierce attacks along the front line in Ukraine’s east. Early on Monday, Russia carried out its third large-scale bombardment of Ukraine in a week, with explosions ringing out in Kyiv and several other cities after a volley of missiles was fired on the first day of the school year.

The nationwide barrages of missiles and drones have been among the largest since the start of Russia’s invasion.

In an effort to undermine Russia’s ability to supply its forces with fuel and cut into the energy revenues that fund the Kremlin’s war effort, the Ukrainian military has for months been targeting Russian oil and gas facilities with attacks. But the campaign has not yet had a demonstrable effect on the fighting inside Ukraine, where Russian forces made steady gains throughout the summer in the eastern Donbas region.

Ukraine had hoped that the long-awaited arrival of Western-supplied F-16 fighter jets would assist in repelling Russian attacks and forces. That effort suffered a blow last week when one of the warplanes crashed while defending against an intense Russian aerial attack, in what may have been a friendly-fire incident.

In an attempt to force Russia to divert forces away from eastern Ukraine, officials in Kyiv ordered an incursion into the Kursk region of Russia in early August. While Russia did send reinforcements to the region, the troops were not sent from eastern Ukraine.

Instead, Russia has pressed on in Ukraine’s east, advancing on the city of Pokrovsk, where the local authorities have urged civilians to evacuate. President Volodymyr Zelensky of Ukraine — who on Tuesday said the Ukrainian offensive in Kursk was going “according to plan” — has sent reinforcements to Pokrovsk, a vital transport and logistics hub for Ukrainian forces in the Donbas region.

The capture of Pokrovsk by Russian forces would be their biggest gain in the region since they seized the cities of Marinka and Avdiivka in January and February after intense ground fighting and bombardment.

It also would bring Russian forces one step closer to achieving a key goal for Mr. Putin: full control of the Donbas region.

Marc Santora contributed reporting.