“The situation has escalated out of control,” Mr. Hochstein told reporters in Beirut, the Lebanese capital. He said that the White House aimed to reach “a comprehensive agreement” that would see the full implementation of U.N. Security Council Resolution 1701, which ended the last major war between Israel and Hezbollah in 2006.

That agreement, which called for U.N. peacekeepers and the Lebanese military to be the only armed forces operating in southern Lebanon, is today widely considered a failure.

In the years since, Iranian-backed Hezbollah has only entrenched itself militarily along Israel’s northern border, amassing a vast arsenal of rockets and missiles. Israel, too, has long been accused of violating Lebanon’s sovereignty, even before embarking on a ground invasion this month.

The U.N. resolution “was successful at ending the war in 2006, but we must be honest that no one did anything to implement it. The lack of implementation over those years contributed to the conflict that we are in today,” Mr. Hochstein said after meeting with Lebanon’s parliament speaker, Nabih Berri, a key interlocutor between the United States and Hezbollah.

Mr. Hochstein also met on Monday with the caretaker prime minister, Najib Mikati, and the commander of the Lebanese armed forces.

His visit was part of a renewed flurry of U.S. diplomatic efforts in the Middle East coming this week. It follows Israel’s killing of Yahya Sinwar, the leader of Hezbollah’s ally Hamas, whose death the Biden administration hopes will pave the way for a cease-fire in Gaza. Secretary of State Antony J. Blinken was scheduled to depart later on Monday for another trip to the Middle East, which will include a stop in Israel, the State Department said.

Hopes for calm, however, appear premature. Israeli forces have continued a deadly offensive against Hamas in northern Gaza, and heavy Israeli airstrikes overnight targeted Hezbollah’s financial apparatus just hours before Mr. Hochstein’s meetings.

Even as the U.S. envoy spoke to reporters, Hezbollah continued to fire rockets toward northern Israel, following pledges by the group to intensify its attacks against Israel in the wake of Mr. Sinwar’s death.

“This is a really heartbreaking moment for me to be here in Lebanon,” Mr. Hochstein said, adding: “While we spent 11 months containing the conflict, we were not able to resolve it.”

Mr. Hochstein said on Monday that the United States would aid in Lebanon’s efforts to rebuild from Israeli attacks, but only if the U.N. resolution was fully implemented to reduce the chances of conflict breaking out again.

“The world will stand by Lebanon and its leaders if they make the brave and the hard choices that are required at this time,” he said. The comments appeared to be a call for the Lebanese government to push for Hezbollah’s disarmament in southern Lebanon, and for it to deploy more Lebanese troops in its place, as stipulated by the 2006 U.N. resolution.

Hezbollah has pledged repeatedly that only an end to the war in Gaza will bring about peace. Although top Lebanese officials have said the group is on board with implementing the U.N. resolution, its leaders have publicly pledged to escalate their aerial attacks against Israel. And it remains unclear if Hezbollah would agree to withdraw from southern Lebanon — with or without a cease-fire in Gaza.

The missiles were intercepted by Israel’s air defenses along with those of the United States and other allies. The THAAD battery, a mobile defense system, is designed to add another layer of protection to defend cities, troops and installations from short- and intermediate-range ballistic missiles.

Mr. Austin said on Monday that the THAAD system was in place in Israel. “We have the ability to put it into operation very quickly,” he told reporters traveling with him to Ukraine.

It is the first time that U.S. troops — about 100 of whom the Pentagon said it was sending to help operate the system — have been deployed to Israel in this way since the Hamas-led Oct. 7, 2023, attacks. Their arrival comes as Israel wages war in Gaza and Lebanon against militia forces backed by Iran. Israel has also struck the Iran-backed Houthi militia in Yemen in recent months and Iran itself earlier this year.

However, it is not the first time that the United States — already Israel’s main military supplier — has boosted its military presence in the Middle East in support of Israel since the Oct. 7 attacks. Shortly after Israel went to war in Gaza in response to the attacks, the United States sent warships to the Persian Gulf and a THAAD battery and Patriot missile defense systems to unspecified locations.

There are currently more than 40,000 U.S. troops in the region, and the Pentagon said in late September that between 2,000 and 3,000 more were being sent to bolster their security.

The THAAD system, which can operate above the atmosphere, is designed to intercept ballistic missiles is also able to intercept debris from downed missiles before it hits the ground, where it can inflict casualties and damage.

President Biden and other U.S. officials say that Mr. Sinwar’s killing could create new opportunities for diplomacy, especially around the long-stalled effort to reach a cease-fire in Gaza that would free hostages held by Hamas and allow for a surge of humanitarian aid to the Palestinians trapped there. But Hamas and Israeli leaders have vowed to fight on, and many analysts doubt that a deal has moved within reach.

Mr. Blinken will arrive in the region at a time when it is bracing for Israel to attack Iran in retaliation for an Iranian ballistic missile barrage on Israel earlier this month. American and Israeli officials have been discussing the response in recent weeks, and Israeli officials have told Washington that they will refrain from attacks on Iranian nuclear or energy sites that could lead to dramatic escalation between the countries.

Mr. Blinken will have several other agenda items during his trip, including planning for the governance and security of Gaza after Israel’s military campaign in the territory ends, the State Department spokesman, Matthew Miller, said in the statement announcing the travel.

Mr. Biden previewed that part of Mr. Blinken’s trip on Thursday, telling reporters that he had spoken with Prime Minister Benjamin Netanyahu of Israel about it. “We’re going to work out what is the day after now — how do we secure Gaza and move on?” Mr. Biden said.

As Israel continues to pound southern Lebanon in a separate campaign against the Iran-backed militia Hezbollah, Mr. Blinken will also discuss “the need to reach a diplomatic resolution to the conflict,” Mr. Miller’s statement said.

The Biden administration has also spent more than two years pursuing a wider regional deal in which Saudi Arabia and Israel would establish formal diplomatic relations for the first time if Israel committed to the creation of a Palestinian state and the U.S. entered into a security agreement with Saudi Arabia.

With Israel still fighting in Gaza, and now at war in Lebanon, the prospects for such a deal during Mr. Biden’s presidency appear slim at best. But Mr. Blinken insisted last month that it was still a realistic goal.

It operates as a lender and financial services provider for civilians in many areas of Lebanon, where the traditional banking sector is in shambles. Many of its branches are situated on the ground floors of residential buildings, and it is deeply embedded in the Shiite Muslim communities it serves.

On social media on Sunday night, Avichay Adraee, the Arabic spokesman for the Israeli military, warned residents of Lebanon to evacuate buildings near the infrastructure of Al-Qard al-Hasan around Beirut and across southern and eastern Lebanon, saying that the organization “is involved in financing the terrorist activities of the Hezbollah organization against Israel.”

Soon after, the sounds of explosions could be heard ringing across Beirut, the Lebanese capital. A New York Times reporter saw dense plumes of black smoke rising in the near distance after the strikes.

The strikes marked an apparent escalation of Israel’s war against Hezbollah, with a senior Israel intelligence official saying the targeting of the banking system — rather than weapons depots or command and intelligence centers — was intended to disrupt Hezbollah’s day-to-day operations, undermine its support in Lebanese communities and hamper its ability to rebuild.

The financial organization has about 30 branches across Lebanon, including in the Dahiya, a densely packed area adjoining Beirut where Hezbollah holds sway.

Israel, the United States and others say that the group, despite its stated aims, serves as a front for Hezbollah financing. The group “purports to serve the Lebanese people” but in practice “illicitly moves funds through shell accounts and facilitators,” the Treasury Department said in 2021 when it was sanctioning individuals involved in what it called Hezbollah’s “shadow banking” network.

“In the coming days, we will reveal how Iran funds Hezbollah’s terror activities by using civilian institutions, associations, and NGOs that act as fronts for terrorism,” Rear Adm. Daniel Hagari, the Israeli military’s chief spokesman, said in a statement on Sunday evening.

Critics of the group say the organization allows Hezbollah to build up its influence with citizens in Lebanon while hobbling the state and putting Lebanon’s banks at risk of foreign sanctions.

A senior Israeli official speaking on condition of anonymity to discuss sensitive matters said that Israel aims to disrupt Hezbollah’s day-to-day financial operations, including paying salaries of Hezbollah’s operatives, which all run through Al-Qard al-Hasan, and to undermine the trust between Hezbollah and the many Lebanese Shiite Muslims who use the branches as an alternative banking service.

Al-Qard al-Hasan said in a statement on Sunday that Israel had exhausted “its bank of objectives and has chosen to threaten and target Al-Qard al-Hasan, the non-profit organization.”

Lebanon is still reeling from a severe financial and economic crisis that began in 2019.

In October of that year, the country was rocked with protests calling for a new government, leading to the prime minister’s resignation.

But the government and the country have yet to recover — and the financial crisis was exacerbated in the years that followed, first by the Covid-19 pandemic, and then by a massive explosion in the port of Beirut in the summer of 2020. Desperate Lebanese citizens have at times even tried to hold up banks where they are customers in an effort to get their money.

Last year, Hezbollah began launching attacks at Israel in solidarity with Hamas after that group’s Oct. 7 attacks on Israel that ignited the war in Gaza. Israel and Hezbollah traded fire for many months in a steady exchange of strikes that seemed, until last month, to be designed to avoid an all-out war.

But Israel in September stepped up its attacks against Hezbollah, targeting its commanders and infrastructure in a series of intense strikes in and near Beirut and throughout southern Lebanon; more than 2,400 people have been killed in Lebanon since October 2023, with the vast majority of those deaths occurring in the recent uptick in Israeli attacks. In October, Israel also launched a ground invasion into southern Lebanon that has led to the displacement of about a million people in Lebanon, according to local authorities.

On Sunday, residents of areas near branches of Al-Qard al-Hasan began fleeing after the evacuation warnings from Israel. Fatima Jneideh said she had evacuated her home just a few meters from a branch location in the Dahiya, an area near Beirut where Hezbollah holds sway. “My brother is still home,” she said. “He refused to leave.”

Isabel Kershner and Hwaida Saad contributed reporting from Beirut and Jerusalem.

The leaked documents, which began circulating on Friday on the Telegram app, were prepared in recent days by the National Geospatial-Intelligence Agency, which is responsible for analyzing images and information collected by American spy satellites.

The documents, which are highly classified, offer interpretations of satellite imagery that provide insight into a potential strike by Israel on Iran in the coming days.

For weeks, an Israeli attack has been anticipated in retaliation for the Iranian missile assault on Oct. 1. Iran’s Islamic Revolutionary Guards Corps said that the strike was in retaliation for the assassinations of Hezbollah’s leader, Hassan Nasrallah, in Lebanon; Hamas’s political leader, Ismail Haniyeh, killed in Tehran in July; and an Iranian commander.

The leaked documents offer a window into intense American concerns about Israel’s plans. U.S. officials are working to ascertain just how much material was leaked, and believe it was disclosed by a low-level government official.

The documents are dated Oct. 15 and represent only what analysts looking at satellite imagery could determine at that time.

Mr. Johnson said that he had spoken to Israel’s prime minister, Benjamin Netanyahu, on Saturday “to encourage him,” and said the United States should stand behind Israel.

“We cannot equivocate,” he said. “We can’t appease Iran. Now is the time for a maximum pressure campaign.”

On Friday, President Biden was asked in Germany whether he knew when Israel planned to strike and what kind of targets it had chosen. “Yes and yes,” he said, declining to say more.

But his statement seemed to suggest that he and Mr. Netanyahu had reached some kind of understanding about what kind of targets would be hit; previously, Mr. Biden called on Israel to avoid Iran’s nuclear sites and its energy facilities. The president has repeatedly raised concerns that if those targets, Iran’s crown jewels, were destroyed, the conflict would quickly escalate.

Mr. Johnson’s office did not respond to a request for comment on the briefing on Sunday.

Julian E. Barnes, Ronen Bergman and David E. Sanger contributed reporting.