WASHINGTON—The Biden administration is urgently pressing for Israel and Hezbollah to pause their escalating aerial attacks into and from Lebanon for 21 days, hoping to head off a full-scale ground war that appears increasingly likely, according to U.S. officials.

Despite a growing buildup along Israel’s northern border, U.S. officials think Prime Minister Benjamin Netanyahu ’s government doesn’t want a wider war and is looking for a diplomatic resolution and that Hezbollah wants breathing room after Israel decimated its leadership and degraded its weapons arsenal in recent weeks.

The U.S. and France in a joint statement called for a 21-day pause in the fighting on Israel’s northern border. Senior Biden administration officials told reporters Wednesday night that now was the right time to call for a cease-fire, hinting strongly that Hezbollah and Israel would eventually agree to the proposed deal, though they have yet to confirm their acceptance.

“The situation between Lebanon and Israel since Oct. 8, 2023, is intolerable and presents an unacceptable risk of a broader regional escalation,” a statement by the U.S. and France, joined by allied nations, said. “This is in nobody’s interest, neither of the people of Israel nor of the people of Lebanon.”

Secretary of State Antony Blinken first discussed the possibility of this proposal with his French counterpart on Monday, a U.S. official said. He spent the next two days on the margins of the U.N. General Assembly shuttling between European and Arab partners on the text, the official continued, including getting agreements from the leaders of Qatar and Saudi Arabia.

Blinken and Amos Hochstein , the White House envoy tasked with brokering a peace between Hezbollah and Israel, discussed the idea with Lebanese Prime Minister Najib Mikati throughout the week.

“We were able to generate significant support from Europe as well as the Arab nations…it’s important the war does not widen,” President Biden told reporters Wednesday night.

Two senior administration officials insisted that a cease-fire between Israel and Hezbollah could provide necessary diplomatic space for Israel and Hamas to agree to their own pause, a deal that has eluded the Biden administration for months.

Arab officials said the U.S. plan envisions a halt in attacks by Hezbollah and Israel, followed by a U.S.-led diplomatic effort to reach a more permanent settlement, which would address land disputes along the Israel-Lebanon border and reconstruction of areas of southern Lebanon damaged in airstrikes.

At the same time, negotiators would resume talks on a cease-fire between Israel and Hamas in Gaza, in hopes that a halt in fighting there would ease the pressure on Hezbollah to keep up its rocket attacks on northern Israel, the Arab officials said.

But the window of opportunity to prevent a war is closing, U.S. officials acknowledged.

Hezbollah’s leadership has vowed not to stop its attacks across the border until Israel halts its campaign in Gaza.

Israel’s military pressure on Hezbollah is aimed at getting it to pull back to the Litani River, 18 miles from the border, and to accept a cease-fire. The recent Israeli attacks have dealt significant damage to the group’s senior leadership, its elite Radwan forces, and its missile and rocket capabilities, according to a person familiar with the discussions.

Hezbollah is also under pressure from Lebanese civilians, “who don’t want their country to be destroyed like Gaza,” the person said.

“Israel has consistently stated that it will give a diplomatic solution a chance, and this remains the case,” an Israeli official said Wednesday.

Arab negotiators and even some U.S. officials aren’t optimistic, noting similar failed efforts to reach a cease-fire deal between Israel and Gaza.

The U.S. doesn’t speak directly to Hezbollah, which it considers a terrorist group, and has enlisted Egypt, Qatar and others to help broker an agreement, Arab negotiators said.

On Wednesday, Israel called up at least two reserve brigades for the north, and the commander of its forces in the north warned of a potential ground invasion of Lebanon. Hezbollah launched more rockets into Israel, along with a ballistic missile aimed at Tel Aviv on Wednesday that was intercepted, its deepest attempted strike yet.

U.S. officials said they haven’t seen signs that a large-scale Israeli ground invasion of southern Lebanon was imminent. Israel could, however, fairly rapidly put additional forces in place for such an assault, they added.

But if Israel decides on a ground incursion, the military campaign will be focused on Hezbollah and military targets, according to the person familiar with the discussions.

For the White House, the push to halt the fighting is especially urgent, with the American presidential election seven weeks away and four months left before President Biden leaves office.

Israel has raised the intensity of its military operations against Hezbollah over the past week in hopes of persuading the militia to stop firing on Israel’s north and allowing tens of thousands of displaced residents to return to their homes there.

“We’re continuing up the escalatory ladder,” said Jonathan Panikoff, former deputy U.S. national intelligence officer for the Near East. “The challenge is, U.S. leverage remains quite low,” said Panikoff, now at the Atlantic Council think tank.

Since the Hamas attacks on Israel on Oct. 7, the U.S. and its allies have sought to prevent the Gaza conflict from expanding into a regionwide war between Israel and Iranian-backed proxies.

“An all-out war is possible, but I think there is also the possibility, we’re still in play, to have a settlement that could fundamentally change the whole region,” Biden said Wednesday on ABC’s “The View” program. “I am using every bit of energy I have, with my team…to get this done.”

Blinken and other top officials have spent the past three days at the United Nations General Assembly in New York trying to find a diplomatic solution, according to one of the U.S. officials, raising ideas with European and Arab partners, the official said.

With a wider war looming, Netanyahu has delayed his arrival in New York to attend the annual U.N. gathering, though he was planning to arrive Thursday morning, according to Danny Danon , the Israeli ambassador to the U.N.

Israel is open to discussing ways to de-escalate the conflict, Danon told reporters. “As we speak, there are important forces trying to come up with ideas,” he said. “We aren’t eager to start any ground invasion anywhere…We prefer a diplomatic solution.”

Retaliatory Israeli airstrikes against Hezbollah have killed at least 564 people since Monday, and forced thousands of civilians to flee, according to Lebanon’s Health Ministry. It said another 1,800 have been injured. Iran-backed Hezbollah has lobbed rockets into northern Israel for almost a year, forcing more than 60,000 Israelis from their homes, the Israeli government has said.

The Biden administration, which at times has been critical of Netanyahu’s military campaign in Gaza, has declined to critique the offensive in Lebanon.

“Israel understandably, legitimately wants a secure environment so people can return home,” Blinken said on CBS . “The best way to get that is through diplomacy, an agreement to pull back forces.”

Write to Lara Seligman at lara.seligman@wsj.com , Nancy A. Youssef at nancy.youssef@wsj.com and Summer Said at summer.said@wsj.com