“It’s unfathomable. You can’t grasp such a thing,” said Keren Doron, 54. The blast that shook her house was so strong, she said, that it cracked some of the walls and shook window blinds loose.

Like millions of Israelis, Ms. Doron, her husband and her daughter spent Tuesday evening into Wednesday morning huddled in fortified rooms, hoping and praying that the strikes would not harm them.

No injuries were reported, said Amir Kochavi, the mayor of Hod Hasharon, but more than 100 homes were damaged by the barrage on Tuesday night. He said that the authorities had yet to find a major metal fragment, but they found particles around the impact site containing explosives they believed to be part of a warhead.

Ms. Doron lives mere feet from the site, and on the footpaths of the homes that ring the park lay remnants of ravaged roofs and shattered windows. In all, Mr. Kochavi said, 15 homes in Hod Hasharon have been declared uninhabitable.

Maj. Zacai Shriki, a liaison from the Israeli military’s Home Front Command, said the city appeared to be the hardest hit by Iran’s attack.

Just a few feet from where the missile fragment landed, Ms. Doron’s daughter, Tom, 11, attends the elementary school that was damaged. One classroom’s ceiling had caved in, and windows across the small campus were blown out.

“It’s unbelievable that I stood right here yesterday, never thinking something like this would happen to my school,” Tom said.

One of the rockets severely damaged a school in the southern city of Gedera, but there were no reports of injuries.

Debris from one intercepted missile landed near Arad in southern Israel. On Wednesday, people climbed atop it.

Although most of the missiles were intercepted, falling debris shattered windows and glass in a building in Tel Aviv.

Sameh al-Asali was a Palestinian from the Gaza Strip who had come to live in the city of Jericho in the Israeli-occupied West Bank. On Tuesday, a fragment of an Iranian missile fell on him, making him the only person known to be killed in the attack targeting Israel.

Debris also fell in the West Bank city of Hebron, where Palestinians on Wednesday inspected the mangled metal of what appeared to be part of an Iranian missile.

The military did not specify where the soldiers were killed, saying only that they “fell in battle in southern Lebanon” on Wednesday.

Five of the eight were members of the elite Egoz Unit, which the military had said earlier in the day was engaged in “targeted operations in several areas of southern Lebanon,” including “close-range engagements” with Hezbollah militants.

“I would like to send my condolences from the bottom of my heart to the families of our heroes who fell today in Lebanon,” Prime Minister Benjamin Netanyahu said in a statement.

In a series of statements posted online, Hezbollah said it had fought Israeli soldiers on Wednesday in the border villages of Yaroun, Odaisseh and Maroun al-Ras.

The group also posted video that showed two military helicopters evacuating soldiers from a dry, grassy field, including two people on a stretcher. But it did not say where the video had been taken.

Maroun al-Ras, which was the scene of a major battle during Israel’s 2006 invasion of Lebanon, is roughly one mile from the Israeli town of Avivim, which Hezbollah said it had targeted with “a salvo of rockets” earlier in the day. Avivim was evacuated last year because of similar attacks.

In Yaroun, Hezbollah said it had detonated an explosive device on Wednesday afternoon, resulting in injuries to Israeli soldiers. The Israeli military did not comment on the report of injuries, and it could not be independently verified.

Al-Manar, a television network owned and operated by Hezbollah, said fighters from the group’s elite Radwan Force had ambushed Israeli soldiers near Odaisseh after they crossed the border from the Israeli village of Misgav Am.

Lebanon’s army — which is not a party to the fighting between Israel and Hezbollah — said in a statement that Israeli forces had crossed the border and traveled roughly a quarter of a mile inside Lebanon in the areas of Yaroun and Odaisseh, “then withdrew after a short period.”

The Israeli military identified the eight soldiers who have been killed as Capt. Eitan Itzhak Oster, 22, Capt. Harel Etinger, 23, Capt. Itai Ariel Giat, 23, Major Noam Barzilay, 22, Major Or Mantzur, 21, Major Nazar Itkin, 21, Sergeant Almken Terefe, 21, and Sergeant Ido Broyer, 21. It did not identify the wounded soldiers.

The gunman Mr. Kraitman encountered was one of two Palestinians who the Israeli authorities said killed seven people and injured at least 16 others in an attack that began on a commuter train in the Jaffa neighborhood in Tel Aviv and then continued on Jerusalem Boulevard, a tree-lined major thoroughfare in the area.

The police did not confirm the account of Mr. Kraitman, who was shown on a video captured by a bystander firing a handgun. The police described the attack as an act of terrorism and said that one gunman was killed at the scene while the other was severely injured. No group immediately claimed responsibility for the attack.

On Wednesday, the police identified their suspects as two Palestinian men from the West Bank town of Hebron: Ahmed Himoni, 25, and Muhammad Mask, 19, who was killed.

The police said several people had been arrested in Hebron and Jerusalem overnight “for being involved in assisting the terrorists in purchasing weapons and entering Israel.”

The attack was one of the deadliest in Tel Aviv in recent years. It occurred amid escalating violence in the region, with Israeli forces initiating a ground operation inside Lebanon against the Iranian-backed Hezbollah militia, Iran firing at least 180 ballistic missiles at Israel, and Israel’s fighting a war against Hamas in Gaza and stepping up raids in the occupied West Bank.

Mr. Kraitman served for six months in Gaza and said that he believed the experience had helped him to respond decisively during the attack on Tuesday night. But he said it had been hard to tell at first where the shots were coming from.

“I rushed forward, crossed the light rail tracks, and saw a wounded man running,” Mr. Kraitman recalled.

He then spotted the two gunmen, who he said had paused their shooting and were talking to each other. The gunmen split up, he said, and one dressed all in black, ran toward him. Mr. Kraitman said he shot the gunman at close range.

“I think I surprised him,” Mr. Kraitman said.

Police and other security forces arrived shortly after. The second gunman was captured nearby.

Mr. Kraitman said he had seen at least three wounded people on the ground. As he and emergency workers tried to assist the wounded, Mr. Kraitman said, sirens went off, warning of incoming Iranian missiles.

“Anyone who cannot unequivocally condemn Iran’s heinous attack on Israel, as nearly all the countries of the world have done, does not deserve to set foot on Israeli soil,” Mr. Katz said in a statement on Wednesday. “Israel will continue to defend its citizens and uphold its national dignity with or without António Guterres.”

Mr. Guterres has repeatedly condemned the attack by Hamas on Oct. 7 and demanded that all hostages taken from Israel that day be released. He condemned an Iranian missile and drone attack on Israel in April. At the same time, he has also repeatedly called for a cease-fire in Gaza and criticized what he called the collective punishment of Palestinians in the enclave.

Hours after the Israeli statement, Mr. Guterres told an emergency session of the U.N. Security Council that he condemned Iran’s attack.

“As I did in relation to the Iranian attack in April — and as should have been obvious yesterday in the context of the condemnation I expressed — I again strongly condemn yesterday’s massive missile attack by Iran on Israel,” he said.

“These attacks paradoxically do nothing to support the cause of the Palestinian people or reduce their suffering,” he said.

Following the Iranian missile attack against Israel on Tuesday — which was largely thwarted — Mr. Guterres wrote in a post on social media: “I condemn the broadening of the Middle East conflict with escalation after escalation. This must stop. We absolutely need a cease-fire.”

It was not clear whether Mr. Katz’s statement was a direct response to that post by Mr. Guterres.

The Israeli government, which had previously called on Mr. Guterres to resign, has also said that the main U.N. agency that aids Palestinians in Gaza and the West Bank, UNRWA, employs many people who are linked to Hamas and other militant groups, and has called for the agency to be disbanded.

The United States and other governments have condemned Iran for the attack on Tuesday — which Tehran said was in retaliation for the assassinations of leaders of its proxy groups Hamas and Hezbollah — and said they would stand by Israel.

The Security Council was holding an emergency meeting to discuss the attack and the threat of a wider Middle East war.

The intensifying fighting between Israel and Iran and its proxies, especially Hezbollah in Lebanon, is increasing fears about the oil market, but so far those worries are still being outweighed by factors like weak demand in China and increased oil production in the United States and elsewhere.

Traders are also aware that after a year of conflict in the Middle East, there has been little disruption to supplies. Oil prices had been falling steadily in recent months, from above $90 a barrel earlier in the year.

But the threat is growing. Israel, for instance, could attack Iran’s main oil export terminal on Kharg Island in the Persian Gulf, with the aim of denying the country oil revenue.

Iran is a sizable oil producer, pumping about two million barrels a day, or about 2 percent of world supply.

Sanctions limit Iran’s production and restrict sales to countries like China. Still, the loss of Iranian supplies would have an effect.

“China would feel the impact of any disruption most directly,” said Richard Bronze, head of geopolitics at Energy Aspects, a research firm. “But any significant loss of Iranian supply would be felt in the wider market, as Chinese buyers would need to find alternative supplies, increasing competition and pushing up prices.”

Iranian attacks on oil installations in nearby states like Saudi Arabia and the United Arab Emirates would be of greater concern, said Helima Croft, an analyst at RBC Capital Markets, an investment bank.

“Iran and its proxies could potentially target energy operations in other parts of the region in order to internationalize the cost if the current crisis devolves into an all-out war,” she wrote in a note.

So far, the diplomatic rapprochement reached between Iran and Saudi Arabia in 2023 seems to be helping to stave off such drastic actions.

At a briefing for reporters in northern Israel on Tuesday, hours after confirming that an invasion of southern Lebanon had begun, military officials offered some details about the raids, showing videos it said were of Israeli soldiers operating in southern Lebanon and displaying weapons and equipment it said were captured in the incursions. The New York Times could not independently verify all of the events depicted in the videos, or confirm the origin of all of the equipment shown to reporters.

Seven Israeli officers and officials, and a senior Western official, had told The New York Times earlier in the week that the commando raids had focused on gathering intelligence about Hezbollah positions close to the border and on identifying Hezbollah tunnels and military infrastructure, in order to prepare the ground for a wider invasion.

On Tuesday, an Israeli military official, who briefed reporters on condition of anonymity to discuss sensitive military matters, said there had been no direct encounters between Israel’s special operations forces and Hezbollah fighters, and that only one Israeli soldier had been injured in the dozens of cross-border incursions. He said two Hezbollah militants had been killed when they returned to a location that was previously raided by Israeli forces, triggering explosives that had been set to destroy the facility.

During the briefing, the military showed videos from what it said was a tunnel near the Israel-Lebanon border, and displayed kits containing weapons, communication devices and backpacks. A spokesman for the Israeli military, Lt. Col. Nadav Shoshani, said that some of the equipment appeared designed for use by fighters in frontline positions and could have been used in a Hezbollah attack on northern Israel.

Among the weapons shown was a Kornet, a portable guided antitank missile made in Russia, and a communications device of the same model as some of those detonated two weeks ago in mass attacks on Hezbollah widely attributed to Israel. Reporters were shown videos of Israeli soldiers walking through homes and entering tunnels, followed by aerial footage of airstrikes on sites that Israel said served as a tunnel entry point.

To conceal their tunnel construction, said the military official who briefed reporters, Hezbollah militants built them primarily under houses and in forests. Some tunnels, he said, were as long as 150 meters, nearly 500 feet. The official said that no tunnel was found reaching under an Israeli town or city, but he did not say whether any tunnel had crossed the border into Israel.

He said that the Lebanese villages targeted during the covert operations were mostly abandoned and that the military believed nearly all of Hezbollah’s frontline forces had moved farther from the border.

President Biden confirmed on Tuesday that the U.S. military had “actively supported” Israel’s defense in shooting down the waves of incoming missiles, noting that American naval forces stationed in the eastern Mediterranean Sea had done so “at my direction.”

“Make no mistake, the United States is fully, fully, fully supportive of Israel,” Mr. Biden told reporters hours after the attack, praising planning between the two nations in anticipation of the barrage.

Other allies soon followed suit. In a statement late Tuesday evening, John Healy, Britain’s defense minister, said British forces had “played their part in attempts to prevent further escalation in the Middle East.”

“The U.K. stands fully behind Israel’s right to defend its country and its people against threats,” he said, thanking “all British personnel involved in the operation for their courage and professionalism.”

Later, Britain’s Ministry of Defense said that two British Royal Air Force Typhoon jets and an air-to-air refueling tanker were deployed to help deter an escalation of the conflict. They were not equipped to shoot down ballistic missiles and it wasn’t clear exactly what they did, but Britain confirmed they “did not engage any targets.”

On Wednesday, Mr. Healy met with British troops based in Cyprus, who are preparing for the potential of a sea evacuation of British citizens from Lebanon, if air travel became impossible. He will also visit the Royal Air Force Akrotiri base, one of two British military bases on Cyprus, a former colony, that have operated for decades.

Last month, some 700 additional British troops were sent to Cyprus after Israeli strikes on Lebanon, in case of an emergency evacuation. Britain already has two warships stationed in the eastern Mediterranean.

Prime Minister Keir Starmer, in a statement on Tuesday night, said he condemned the “attempt by the Iranian regime to harm innocent Israelis, to escalate this incredibly dangerous situation and push the region ever closer to the brink.”

“It cannot be tolerated,” he added.

The French presidency said on Wednesday that France had “mobilized its military resources” in the Middle East to help Israel counter Iran’s missile attack, but did not provide details.

It said in a statement that President Emmanuel Macron, who convened an overnight defense and security meeting, condemned the missile barrage while urging Israel to end its military operations in Lebanon, where “too many civilians are already victims.”

There are 700 French soldiers stationed in Lebanon as part of UNIFIL, the United Nations force that was established there in 1978. France announced this week that it was sending a helicopter carrier to the eastern Mediterranean in case it had to evacuate some of the roughly 20,000 French citizens who are in Lebanon.

France has a broader presence in the Middle East as well, with military bases in Qatar, Kuwait, Iraq and the United Arab Emirates and the ability to deploy ten Rafale fighter jets from air bases across the region.

On Wednesday, Iran’s foreign minister, Abbas Araghchi, warned that any “third party supporting Israel” would face a “strong response,” Iranian state media reported.

FilterLabs has been tracking attitudes about the militia leader. Support for Mr. Nasrallah, a Shiite Muslim, peaked in Sunni Arab countries in mid-September, when Hamas — a Sunni group — released a letter of support for him from its leader, Yahya Sinwar.

According to the analysis, attitudes toward Mr. Nasrallah began returning to their usual levels across the Middle East after the letter but rose again after the Israeli strike that killed him, reflecting anger toward Israel and enthusiasm for Mr. Nasrallah’s support for Palestinians in Gaza.

Sentiment about Mr. Nasrallah was more positive on news media sites in Lebanon after his death. But FilterLabs found that commentators on Lebanese social media also focused on the damage caused by the Israeli strike.

Mr. Nasrallah, who led Hezbollah for 32 years, was a towering figure across the Middle East. On Saturday, demonstrators in several countries in the region mourned him and condemned Israel’s strikes. But some communities, including in Lebanon, welcomed his death.

The FilterLabs analysis noted worries among some in Lebanon that Hezbollah had courted a war with Israel, a conflict that has caused civilian casualties and threatens to bring further destruction to Lebanon, including its capital, Beirut.

Mr. Teubner said that in the days since Mr. Nasrallah’s death, many in Lebanon have hailed him as a martyr.

“But Lebanon is more negative overall on Nasrallah than the Arab world more generally because their focus has been on the devastation that has occurred and, in all likelihood, will increase with a ground invasion,” Mr. Teubner said.

On Monday, Israel began what it called a limited incursion into southern Lebanon. U.S. officials said that their Israeli counterparts told them they were not planning a full-scale invasion, but the Biden administration remains worried that the Israeli military might get bogged down and remain in Lebanon longer than it planned.

Iran’s strikes on Tuesday, in retaliation for the killing of Mr. Nasrallah, could further shape attitudes in the days to come.

FilterLabs uses a computer model to analyze huge numbers of online posts, from social media sites, news media publications and other internet discussion forums. The model measures the sentiments expressed in postings to determine how public opinion on various subjects has shifted. Since the beginning of the war in Ukraine, the group has tracked Russian attitudes on a variety of topics.

The man with the gruff voice would not listen.

As Israel began a ground invasion of Lebanon on Tuesday, Ain Ebel was among more than two dozen towns along the border that the Israeli military told to evacuate. Although Hezbollah, the Lebanese Shiite group, exercises de facto control over much of the country’s south, the region is peppered with Christian, Druze and Sunni Muslim communities that are not aligned with the group.

Most of Ain Ebel’s homes were already empty, the women and children having fled months ago. Few there could forget that the village had been caught in the crossfire before. In 2006, when Israel and Hezbollah last fought a major war, the townspeople were besieged and had no bread for nearly three weeks.

Those in the village figured this time that they had three options: stay put, try to make it to Beirut, or flee to Rmeish, a nearby village that was not told to evacuate, and take shelter at the Lady of the Annunciation Monastery there. Most considered Rmeish the safest option, and soon honking cars began careering through the streets as they made the three-mile dash to the monastery.

Najib al-Amil, Rmeish’s 72-year-old priest, said the bare brick monastery had sheltered hundreds of Ain Ebel’s residents on Tuesday. Most were later evacuated to Beirut by the Lebanese Army and the Red Cross, although dozens remained overnight, fearful of being caught in the crossfire if they left.

“They are worried,” said Mr. al-Amil. “We are trying to take away their pain.”

Three people from the nearby Christian village of Debel — a couple and their son — were killed early Wednesday in an Israeli strike on their home, Lebanon’s state-run news agency reported.

Now in the Lebanese capital, some residents of Ain Ebel wondered if and when they would return to their beloved village.

“When will I come back? I don’t know,” said Mr. Ashlar. “We don’t know when we will see our homes again. This could take a week. This could take a month. This could take a year — this could take 10 years.”

It was a sentiment felt in towns and villages across southern Lebanon, where Israeli troops were amassing along the border for the first time in nearly two decades.

“Last night, nobody slept,” said Dana Kaydouh, a resident of the border town of Shebaa, which has received similar phone warnings in recent days. After an Israeli strike killed nine members of a neighboring family, she finally packed up and left.

“Everyone is afraid,” she said.