US Secretary of State Antony Blinken, in a big US push for a ceasefire in Gaza, met Israeli Prime Minister Benjamin Netanyahu on Tuesday after Washington called for an end to the war in Lebanon "as soon as possible".

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.

His meetings with Netanyahu and other top officials also come as Israel weighs its response to Iran's October 1 missile attack.

Diplomatic efforts have so far failed to bring an end to both the year-long war in the Palestinian territory Gaza and to its spillover conflict between Israel and Hezbollah.

Hezbollah said on Tuesday there would be no negotiations while fighting continues, and 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 attacks on October 7 last year on Israel 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 Sayed Hassan Nasrallah in an airstrike.

Netanyahu has pledged to annihilate Hamas and recover dozens of hostages held by the group. Hamas says it will only release the captives in return for a lasting ceasefire, a full Israeli withdrawal from Gaza and the release of Palestinian prisoners.

Blinken's week-long trip to the Middle East will also take him to Jordan and Qatar. US officials say he is focusing on plans for rebuilding and governing Gaza after the war, necessary for reaching a ceasefire.

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 the Israeli occupied West Bank.

Blinken also plans to speak to Israeli leaders about the expected strike on Iran and discourage any move that could massively escalate regional conflict, an official on the plane with him said.

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

Israel's retaliatory offensive has killed 42,718 Palestinians, Gaza health authorities say. (Agencies)