In recent days, Israeli commando units have carried out raids into Lebanon, as part of preparations for a broader ground invasion.

Israel says its aim is to secure the northern border, allowing civilians to safely return to their homes, and on Monday, Israeli artillery shelling shook southern Lebanon, sending beige clouds of dust rising over mountain villages.

Despite the thunderous explosions, soldiers and the few remaining civilians in Kiryat Shmona, the northernmost city near the Lebanese border, stayed largely unfazed, perhaps inured to the sounds of war. The city is nearly abandoned, its streets dominated by soldiers, military vehicles, and security personnel.

In fading daylight Monday, a small group gathered at a cemetery for the funeral of 87-year-old Aliza Ohayun.

Midway through the ceremony, a siren wailed, and the mourners took cover between the graves. Then they hastily concluded the service.

“Despite the situation, we didn’t consider burying her elsewhere,” said Ms. Ohayun’s granddaughter, Hufit Lugasi, 43. “This has been her home since she arrived from Morocco as a teenager.”

Several miles south of Kiryat Shmona, in Kfar Blum, an Israeli village that has not been evacuated, Moran Grunter went out for a night jog, saying the exercise eases her mood in the tense atmosphere. Unlike many residents, Ms. Grunter, 44, opposes a ground invasion, she said. “They should operate from the skies,” she said, alluding to airstrikes and shelling. “There’s no need to endanger soldiers’ lives.”

Asaf Tzarfati, a 46-year-old infrastructure project manager from Kiryat Shmona, has been staying in Tel Aviv for a year with his wife and two children to avoid the rockets Hezbollah has been firing into northern Israel. Hezbollah launched the rockets in solidarity with Hamas, escalating cross-border attacks that have displaced tens of thousands on both sides.

Mr. Tzarfati said he believed that the heavy blows Israel has dealt to Hezbollah in recent days — including the assassination of the Hezbollah leader, Hassan Nasrallah — only a ground invasion of southern Lebanon could truly restore safety to northern Israel.

“Residents of the north won’t feel safe until the Israeli military takes over a security strip in southern Lebanon,” Mr. Tzarfati said.

A Pentagon spokeswoman, Sabrina Singh, said the deployment would include multiple fighter squadrons. Other officials said they would include F-15, F-16 and F-22 fighter jets as well as A-10 warplanes, adding substantially to American air capability.

The Pentagon declined to say exactly how many more troops were being deployed. But one official put the number at between 2,000 and 3,000.

The 40,000 American troops already in the region are stationed on bases in Iraq, Syria and other countries. The U.S.S. Abraham Lincoln, in the Gulf of Oman, is on an extended deployment in the region, and a second aircraft carrier, the U.S.S. Harry S. Truman, left Norfolk, Va., a week ago for the Mediterranean as part of a regularly scheduled deployment.

Last week, the Pentagon announced it was deploying additional troops to the region but declined to give a number.

Israeli commando units have made brief incursions into Lebanon in recent days to prepare for a possible wider ground invasion, according to several Israeli officers and officials and a senior Western official. But American officials said on Monday that they believed that the invasion would be limited.

The Israeli and Western officials said the raids were focused on gathering intelligence about Hezbollah’s positions near the border, as well as identifying the Iranian-backed group’s tunnels and military infrastructure, in order to attack them from the air or the ground. The officials spoke on the condition of anonymity to discuss a sensitive military matter. The Israeli military declined to comment.

Hezbollah began attacking northern Israel soon after Hamas, which is also backed by Iran, attacked Israel on Oct. 7. Israel and Hezbollah have been exchanging fire since then.

On Sunday, Defense Secretary Lloyd J. Austin III warned that “should Iran, its partners or its proxies use this moment to target American personnel or interests in the region, the United States will take every necessary measure to defend our people,” according to a Pentagon statement.

For months, the Biden administration and its allies have warned that the Palestinian Authority’s dire financial straits could foreshadow another escalation in the West Bank. Israeli forces have been stepping up raids targeting militants in which they ripped up roads and wrecked shops and homes in the territory.

The Saudi foreign ministry announced on Sunday night that it would send a monthly aid package to the country’s “brothers in Palestine” to alleviate the “humanitarian situation in the Gaza Strip and its surrounding areas,” without specifying the amount or intended recipients. The commitment was made during a recent visit by the president of the Palestinian Authority, Mahmoud Abbas, to Saudi Arabia, according to one of his aides.

“Prince Mohammed affirmed to the president, Abu Mazen, the kingdom of Saudi Arabia’s support for the Palestinian people politically and materially,” said Mahmoud al-Habbash, a senior adviser to Mr. Abbas. Mr. al-Habbash was referring to the Saudi crown prince, Mohammed bin Salman, and Mr. Abbas, using his nickname.

Saudi Arabia has agreed to deliver $60 million to the Palestinian Authority in six installments, with the first payment expected in the coming days, according to a senior Palestinian Authority official.

The funds will directly support the authority’s budget, said the senior official, who spoke on condition of anonymity to discuss sensitive information.

Four other Palestinian officials and four diplomats, who spoke on condition of anonymity because they weren’t authorized to communicate with the news media, confirmed Saudi Arabia has committed to send tens of millions of dollars to the authority.

With an economic crisis engulfing the West Bank since Hamas-led attacks on Oct. 7, the Palestinian Authority has struggled to cobble together funds to pay its civil servants and security forces, who constitute much of the territory’s labor force.

Israel has frequently refused to transfer tax revenues it collects on behalf of the Palestinian Authority. International aid has also dwindled for the authority, which is viewed by its allies and much of the Palestinian public as both corrupt and ineffectual.

The economic hardship has been compounded by the Israeli authorities’ blocking of tens of thousands of Palestinian laborers from entering its territory since the Oct. 7 attacks. Those laborers had brought billions of dollars annually into the West Bank’s economy.

Experts on the Persian Gulf said that Saudi Arabia’s renewed financial support for the authority was an attempt to stave off its implosion, not an endorsement of its leadership. The deliberations over sending the aid preceded the recent escalation between Israel and Hezbollah by at least several weeks.

“For Saudi Arabia, a two-state solution is essential,” said Hussein Ibish, a senior resident scholar at the Arab Gulf States Institute in Washington. “They’re not saying the Palestinian Authority is a great institution, but they are saying it must not collapse in order to preserve the possibility of establishing a Palestinian state.”

At a meeting on the sidelines of the annual United Nations General Assembly on Thursday, Prince Faisal bin Farhan, the Saudi foreign minister, announced the establishment of an international coalition to push for the two-state solution.

“Implementing the two-state solution is the best solution to break the cycle of conflict and suffering and enforce a new reality in which the entire region, including Israel, enjoys security and coexistence,” Prince Faisal said.

This month, Prince Mohammed said Saudi Arabia would not establish diplomatic relations with Israel before the “establishment of a Palestinian state,” an apparent hardening of his position on an issue that could reshape the diplomatic map of the Middle East.

For decades, the leaders of Saudi Arabia, like those of most other Arab countries, refused to recognize Israel without the creation of a state for the Palestinians. But after 2020, when four Arab states established formal ties with Israel in agreements brokered by former President Donald J. Trump, Prince Mohammed became the first Saudi leader to talk openly about the possibility of Saudi Arabia’s doing the same.

The Biden administration worked to broker the agreement as part of a grand bargain among the United States, Israel and Saudi Arabia. But after Oct. 7, those talks slowly ground to a halt, as the war between Israel and Hamas in Gaza continued without an end in sight.

Ismaeel Naar contributed reporting from Dubai, United Arab Emirates.

After the discussions, U.S. officials, who spoke on the condition of anonymity to discuss sensitive intelligence and diplomatic negotiations, said they believed Israel was planning only smaller, targeted incursions into southern Lebanon. The raids by Israeli special operations forces would be designed to eliminate fighting positions from which Hezbollah has attacked towns in northern Israel.

But Israeli officials assured their American counterparts that they did not intend to follow up those incursions with a bigger operation by conventional forces or by occupying parts of southern Lebanon. U.S. officials said they believed the commandos would quickly pull back after the operations were finished.

Matthew Miller, the State Department spokesman, said Israeli officials told the United States that they were conducting “limited operations focused on Hezbollah infrastructure near the border” between Israel and Lebanon.

“Israel has a right to defend itself against Hezbollah,” Mr. Miller said, adding that “we want to ultimately see a diplomatic resolution to this conflict, one that allows citizens on both sides of the border to return to their homes.”

It is not clear if Israel has made a final decision, and it is possible that a full-scale invasion could still follow targeted raids, despite the White House’s concerns.

On Monday, after the raids became public, U.S. officials said the possibility of “mission creep” remained, and that Israel could decide it needed to support the raids with a larger force. But for now, American officials believe, Israel will not conduct a full-scale invasion.

U.S. officials have tried to prevent a wider regional conflict since the war in Gaza began last October after Hamas-led attacks in Israel.

Israel eventually cut back the intensity of its bombing campaign in Gaza, but months after the U.S. military had urged a shift to more targeted operations. The United States wanted the Israeli military to eschew major combat operations and said that operations in the city of Rafah needed to be more precise. The eventual Israeli operations in Rafah were extensive.

This month, some officials in the U.S. government have watched the Israeli operations against Hezbollah anxiously, fearing that the extensive attacks would provoke Iran to join the fight far more openly. But other officials believe that Israel’s actions have dramatically curbed Hezbollah’s military power. The risk of Iranian intervention remains, American officials said.

Still, to keep the wider conflict in check, American officials want to persuade Israel not to move large numbers of forces into Lebanon, and U.S. and French officials had been pushing for a cease-fire proposal. When Prime Minister Benjamin Netanyahu of Israel authorized the strike on Hassan Nasrallah, the leader of Hezbollah, the cease-fire plan was thrown into question.

At the State Department briefing, Mr. Miller said the proposal unveiled last week, which called for a 21-day cease-fire between Israel and Hezbollah, remained on the table. The United States is also pursuing a long-term diplomatic resolution which would require Hezbollah to withdraw forces from the border in accordance with United Nations requirements that Hezbollah has flouted.

“We should be clear that the burden of that diplomatic resolution falls not just on Israel, but on Hezbollah as well,” he said.

Despite hitting pause on the effort to broker a cease-fire, Americans have tried to convince Israeli officials that a ground invasion would be counterproductive.

American intelligence agencies stuck by their assessment throughout September that any sort of large-scale invasion of southern Lebanon would court disaster. While Israel’s strikes have diminished Hezbollah’s caches of weapons and hurt its ability to launch rocket attacks, the group’s forces maintain dug-in positions in the hilly and easily defended terrain of southern Lebanon.

The Hezbollah tunnel network largely remains intact, and American officials assessed that Hezbollah fighters would be able to move through it quickly to ambush advancing Israeli forces. Many of the tunnels are far bigger than the network Hamas built under Gaza, allowing Hezbollah to move large numbers of missiles and vehicles around southern Lebanon undetected.

Cola is a largely Sunni Muslim neighborhood within the city limits. Lebanon’s health ministry said the blast had killed four people and injured four others.

The Popular Front for the Liberation of Palestine, a militant group based in Lebanon and Gaza, said that three of its members had been killed. On Monday afternoon, the Israeli military claimed responsibility for the blast, saying it had “struck and eliminated” the head of the militant group’s Lebanon branch and an associate. It was the first known Israeli strike in central Beirut since Israel and Hezbollah fought a war in 2006.

Mr. Darwish said he had been asleep with his wife when he woke up to the sound of an explosion and the crash of concrete hitting the sidewalk.

He immediately grabbed a bag of clothes and blankets he had packed days earlier, and he and his wife ran downstairs to their car. They set off for their second home in Lebanon’s northern mountains. The city, they deemed, was no longer safe.

Nearby, Ahmad Qanso, 60, gazed over at the destruction, leaning on his wooden cane. He said he was sleeping under a nearby bridge — one of many Lebanese who have spent nights in the open air in Beirut since Israeli bombardment escalated in recent days — when he woke up to what sounded like an explosion. “I was shocked,” he said.

Mr. Qanso and two of his neighbors arrived in Beirut on Saturday after fleeing their village of Chehabyeh, in southern Lebanon, which has been hit by Israeli airstrikes. “When we first arrived, we thought it was safe here,” he said. “But now, there’s no safety anywhere. There’s not even shelter.”

Speaking from an undisclosed location, Sheikh Qassem called on Hezbollah members to follow contingency plans put in place to ensure that alternate commanders were available if anything happened to the group’s leaders.

He denied reports that Israel’s attacks, which have pounded targets in Hezbollah strongholds across Lebanon over the past week and killed hundreds of people, had significantly damaged the group’s arsenal or reduced its fighting power.

Some Israeli leaders have spoken of the possibility of a ground invasion of southern Lebanon aimed at wiping out Hezbollah’s military infrastructure near the border. Sheikh Qassem said Hezbollah was ready to fight any ground incursion.

“We will confront any possibility, and we are ready if the Israelis decide to enter by land,” he said. “The forces of the resistance are ready for a ground engagement.”

Sheikh Qassem also denied Israeli claims that Mr. Nasrallah had been killed during a large meeting with many other senior officials, saying instead that those killed with him included Ali Karaki, a Hezbollah leader; Abbas Nilforoushan, a senior Iranian military official; Mr. Nasrallah’s head of security; and another close associate.

Israel’s cabinet was expected to discuss on Monday evening whether and when to launch a major ground operation in southern Lebanon, which would be Israel’s first there in nearly two decades. Israel occupied southern Lebanon from 1982 to 2000 and briefly invaded again in 2006, during a monthlong war with Hezbollah.

Officials said that if a broader operation proceeds, Israel was expected to try to destroy Hezbollah military infrastructure near the border, likely in an intense series of cross-border raids, rather than to advance deep into Lebanon and occupy large areas of land. Southern Lebanon is a rugged area, filled with steep valleys in which defenders can easily ambush an invading army, a factor that may have shaped Israeli military planning.

The raids and plans suggest that Israel is seeking to capitalize on Hezbollah’s disarray, after it killed much of the group’s senior leadership in recent weeks, including its secretary general, Hassan Nasrallah. Though much of Hezbollah’s high command is dead, the group still controls much of the Lebanese side of the Israel-Lebanon border, where, Israel says, the group has built an extensive network of military installations, rocket launchers and tunnel networks that pose a threat to residents living in northern Israel.

The Israeli government’s declared goal is to make the border area safe enough for tens of thousands of Israelis displaced by Hezbollah rocket fire over the last year to return to their homes.

Hundreds of thousands of Lebanese civilians have also been displaced by Israeli fire on the other side of the border. Hezbollah and Israel first fought each other during Israel’s occupation of Lebanon in the 1980s, but the current conflict began last October after Hezbollah began firing into Israeli-controlled territory, leading to a low-intensity border war.

For nearly a year, the two sides have been gradually firing deeper into each other’s territory, but they avoided an all-out war until this month, when Israel targeted Hezbollah’s senior leaders and blew up hundreds of Hezbollah’s pagers and radios.

For months, Israeli special forces have also been briefly crossing the border on reconnaissance missions though those were not to prepare the ground for a land invasion, according to five of the officials.

Their approach changed in recent days as the incursions increased in intensity and ambition for a wider maneuver, three of the officials said.

Hezbollah said on Monday that its forces would confront Israeli troops if they mounted a full invasion. The group also denied that its fighting power or arsenal had been significantly damaged in recent weeks by Israel’s bombardments, which have killed hundreds of people, including civilians.

“We will confront any possibility, and we are ready if the Israelis decide to enter by land,” Sheikh Naim Qassem, Mr. Nasrallah’s deputy, said in a televised statement. “The forces of the resistance are ready for a ground engagement.”

Since Israel began escalating the conflict two weeks ago, Hezbollah and its benefactor, Iran, have failed to respond with the intensity that many analysts and officials had anticipated. They assumed that if Israel began assassinating Hezbollah’s senior leadership, the group would begin firing thousands of missiles toward central Israel, overwhelming Israel’s air defense systems and taking out key infrastructure targets, including the Israeli power grid.

Instead, Hezbollah has fired brief barrages of rockets, mostly toward northern Israel, forcing thousands of Israelis to take cover in their bomb shelters but failing to exact significant damage. And Iran has not directly intervened.

Still, American officials said on Monday that they had pressed Israel to avoid a full-scale invasion of Lebanon, amid fears that a more extensive attack would provoke Iran to join the fight far more openly in order to protect its proxy.

After discussions over the weekend with Israeli counterparts, the U.S. officials, who spoke on the condition of anonymity to discuss sensitive intelligence and diplomatic negotiations, said they believed Israel was planning only smaller, targeted incursions into southern Lebanon.

Julian E. Barnes, Ben Hubbard and Gabby Sobelman contributed reporting.

The A.P. released videos from the Lebanese capital on Monday that showed people and emergency workers gathering below a damaged multistory building in the largely Sunni Muslim neighborhood of Cola. There was no immediate comment from the Israeli military.

A militant group based in Lebanon and Gaza, the Popular Front for the Liberation of Palestine, said that three of its members had been killed in the blast in Cola. That claim by the group, which is mostly known for a string of airline hijackings and bombings decades ago, could not be independently verified.

The intensifying cadence of Israeli strikes has stretched deep into Lebanon. Israel has said that most have been directed at Hezbollah, whose leader, Hassan Nasrallah, was killed late Friday by Israeli bombs. But the military has also hit other groups, including a strike against Iran-backed Houthi forces in Yemen.

Euan Ward contributed reporting.