Secretary of State Antony Blinken met Israeli Prime Minister Benjamin Netanyahu on Tuesday in the first big U.S. push for a Middle East ceasefire since Israel killed the leader of Hamas last week - and the last attempt before a presidential election that could upend U.S. policy.

Blinken began his meetings in Israel as Hezbollah launched rockets into Tel Aviv and Haifa and Israeli air strikes pummelled parts of Beirut’s southern suburbs, including an air strike that caused a multi-storey building to entirely collapse and sent a fresh wave of panicked residents fleeing.

Repeated diplomatic efforts have failed to bring an end to both the year-long war in the Palestinian territory of Gaza and to its spillover conflict between Israel and the Lebanese Iran-backed armed group Hezbollah.

Blinken, on his 11th trip to the region since the Gaza war erupted, faces a daunting mission.

Hezbollah said on Tuesday there would be no negotiations while fighting continues and it claimed responsibility for a drone attack on Netanyahu’s holiday home on Saturday.

Washington hopes the death of Hamas leader Yahya Sinwar - Israel’s most wanted man, blamed for triggering the year of warfare by planning the deadly attack on Oct. 7 last year on Israeli territory - will provide a new opportunity for peace.

But Israel has so far shown no sign of relenting in its military campaigns even after assassinating several leaders of Iran’s allies Hamas and Hezbollah, which lost its powerful secretary-general Hassan Nasrallah in a Sept. 27 airstrike.

In Gaza on Tuesday, the U.N. Palestinian refugee agency UNRWA called for a temporary truce to allow civilians to leave areas in the north of the enclave where Israeli forces were hunting down Hamas militants.

Gaza health officials said more than 20 people had been killed by Israeli forces. Dozens of corpses lay on roadsides and under rubble, they said.

"Hospitals ran out of coffins to prepare the dead," said Munir Al-Bursh, director of the Gaza health ministry.

Sirens in Tel Aviv

Blinken was meeting Netanyahu and other officials at the start of a week-long trip that will also take him to Jordan and Qatar. U.S. officials say he is exploring plans for rebuilding and governing Gaza after the war, key to reaching a ceasefire.

Iran and its allies - Lebanon’s Hezbollah, Yemen’s Houthis, armed groups in Iraq and Hamas in Gaza - have said that their "Axis of Resistance" against Israeli and U.S. interests will emerge victorious.

The Houthis said on Tuesday they had targeted an Israeli military base in Tel Aviv using ballistic missiles in solidarity with Hezbollah in Lebanon and Hamas in Gaza.

Hours before Blinken landed, air raid sirens sounded in Tel Aviv and other areas of central Israel after Hezbollah fired missiles at what it said were Israeli military targets near Haifa and Tel Aviv. The missiles were an apparent demonstration that Hezbollah’s capabilities have survived Israel’s biggest onslaught in decades of hostilities.

The conflict has spread to Lebanon over the past month, with Israel launching a ground campaign and intensified air assaults against Hezbollah, which had been firing across the frontier for a year in solidarity with the Palestinians. Israel’s offensive has driven 1.2 million Lebanese from their homes.

During a night of heavy strikes on south Lebanon and the southern suburbs of Beirut, Israel struck the area near Beirut’s Rafik Hariri hospital, Lebanon’s main state medical facility. Lebanese authorities said 13 people were killed.

The Israeli military said the hospital itself had not been targeted and was not affected. Director Jihad Saadeh said the hospital was damaged because of an Israeli attack near it.

Hamas, which is still holding scores of hostages in Gaza seized in its Oct. 7, 2023 raid on Israel, refuses to release them without an Israeli pledge to end the war.

Israel says it will not halt fighting until the Islamist militant group is completely destroyed in the enclave, which has been largely reduced to ruins by Israeli bombardment.

Washington and other allies hope Israel’s killing of Sinwar in a firefight last week could provide a breakthrough by making it easier for Netanyahu’s far-right government to assert that its objectives have been achieved in Gaza.

But diplomats and other sources say Israel is pressing to lock in a strong position before a new U.S. administration takes over following the Nov. 5 election between Vice President Kamala Harris and former president Donald Trump.

Israeli retaliation against Iran

State Department officials said Blinken intended to raise the issue of what happens in Gaza when the war ends, focusing on security, governance and reconstruction. Washington has long said it ideally wants Gaza reunited with the West Bank under a government run by the Palestinian Authority, which now exercises limited self-rule in that Israeli-occupied territory.

Blinken will also discuss Israel’s anticipated retaliation for a ballistic missile attack launched by Iran on Oct. 1, a senior State Department official said.

Allies are worried that Israel’s response could disrupt oil markets and ignite a full-blown war between the arch-enemies.

The Gaza war began after Hamas-led fighters attacked Israeli communities on Oct. 7 last year, killing around 1,200 people and capturing more than 250 hostages, according to Israeli tallies.

Israel’s subsequent air and ground war in Gaza has killed 42,718 Palestinians, the enclave’s health authorities say.