Israel’s military chief told troops on Wednesday that air strikes in Lebanon would continue in order to destroy Hezbollah infrastructure and to prepare the way for a possible ground operation by Israeli forces.

Even as he spoke, sources said the United States had started a diplomatic push to stop the fighting in both Gaza and Lebanon, and that proposals were being hammered out at the U.N. General Assembly in New York.

U.S. President Joe Biden told ABC television that all-out war was possible, but added: “We’re still in play to have a settlement that can fundamentally change the whole region.”

Israel on Wednesday widened its airstrikes in Lebanon and shot down a missile that the Iranian-backed Hezbollah movement said it had aimed at the headquarters of the Mossad intelligence agency near Israel’s biggest city, Tel Aviv.

“You hear the jets overhead; we have been striking all day,” General Herzi Halevi told Israeli troops on the border with Lebanon, according to a statement from the military.

“This is both to prepare the ground for your possible entry and to continue degrading Hezbollah.”

World leaders expressed concern that the conflict - running in parallel to Israel’s war in Gaza against the Palestinian Hamas movement, also backed by Iran - was escalating rapidly as the death toll in Lebanon rose and thousands fled their homes.

U.S. Secretary of State Antony Blinken said Washington and its allies were working tirelessly to avoid a full-blown war between Israel and Hezbollah, which has said it will not back down until the Gaza war ends.

Two Lebanese officials, two Western diplomats, a source familiar with Hezbollah’s thinking and a source briefed on the talks, all of whom declined to be named, said Washington was leading a new diplomatic push that for the first time covered both conflicts - in Gaza and Lebanon.

Ceasefire proposals

Three Israeli sources said the United States and France were working on ceasefire proposals to resolve the escalating fighting in Lebanon, which Hezbollah began in support of Hamas in Gaza, but that so far no significant progress had been made.

“Risk of escalation in the region is acute … The best answer is diplomacy, and our coordinated efforts are vital to preventing further escalation,” Blinken said at a meeting with Gulf Arab state officials and ministers in New York.

Israeli airstrikes this week have targeted Hezbollah leaders and hit hundreds of sites deep inside Lebanon while the group has fired barrages of rockets into Israel, where hundreds of thousands have fled the border region.

On Wednesday, Israel said its warplanes were hitting south Lebanon and the Bekaa Valley, a Hezbollah stronghold further north, and that it was calling up two more reserve brigades for operations on the northern border.

“This will enable the continuation of combat against the Hezbollah terrorist organization, the defence of the State of Israel, and create the conditions to enable the residents of northern Israel to return to their homes,” it said.

In a brief video message that made no comment on U.S.-led efforts to secure a ceasefire deal, Israeli Prime Minister Benjamin Netanyahu said Hezbollah was being hit harder than it could ever have imagined, and repeated a vow to return tens of thousands of Israelis to their homes in northern border areas.

Lebanese hospitals have filled with the wounded since Monday, when Israeli bombing killed more than 550 people in Lebanon’s deadliest day since its civil war ended in 1990. At least 51 people were killed and at least 223 wounded in Wednesday’s strikes, according to the Lebanese health minister.

Hezbollah said it had aimed a missile at Mossad headquarters “in support of our steadfast Palestinian people in the Gaza Strip … and in defence of Lebanon and its people”.

It blamed Mossad for assassinations of its leaders and has also accused it of booby-trapping Hezbollah members’ pagers and radios that exploded last week, killing 39 people and wounding nearly 3,000. Israel has neither confirmed nor denied involvement.

Israel denies missile was heading for Mossad HQ

Israeli officials said a “heavy missile” had headed towards civilian areas in Tel Aviv, not Mossad’s HQ, before being shot down.

Israel has expanded the zones in Lebanon that it had been striking since Tuesday night, with attacks for the first time on the beach resort of Jiyyeh, just south of Beirut.

It also attacked Bint Jbeil, Tebnin and Ain Qana in the south, the village of Joun in the southerly Chouf district near Sidon, and Maaysrah in the northern Keserwan district.

As many as half a million people may have been displaced in Lebanon, its foreign minister said. In Beirut, thousands of people displaced from southern Lebanon were sheltering in schools and other buildings.

More than 60 people were evacuated from the Christian town of Alma Chaab, along the border, following strikes overnight.

“At least two houses were completely destroyed but thankfully they were empty and we had no deaths,” said Milad Eid, a resident.

Israeli authorities said the Galilee region of northern Israel was hit by heavy Hezbollah barrages on Wednesday morning.

In the Israeli town of Safed, an assisted living facility was hit but no injuries were reported, the authorities said.

Near-daily exchanges of fire in the Israel-Lebanon border area started after war broke out last October between Israel and the Palestinian militant group Hamas in the Gaza Strip on Israel’s southern border.