US Secretary of State Antony Blinken will make another push for a ceasefire when he heads to the Middle East, seeking to kick-start negotiations to end the Gaza war and also defuse the spillover conflict in Lebanon.

Blinken's trip to the region on Monday, his 11th since the attack on Israel by the Palestinian militant group Hamas on October 7, 2023, that triggered the Gaza war, comes as Israel intensifies its military campaign in Gaza, and in Lebanon against the Iran-aligned Hezbollah militia.

Israel has raised the stakes by assassinating the leaders of Hezbollah in Lebanon, including its veteran secretary-general Sayyed Hassan Nasrallah, and of Hamas in Gaza while showing no sign of reining in its ground and aerial offensives.

Killing Hamas leader Yahya Sinwar last week after a year-long search was a major victory for Israel. But its leaders say the war must go on until the Islamist group is eliminated as a military and security threat to Israel.

Iran and its allies have said Sinwar's death in a gunbattle with Israeli soldiers in Gaza will strengthen their resolve.

Blinken will discuss with regional leaders the importance of ending the war in Gaza, ways to chart a post-conflict plan for the Palestinian enclave, and how to reach a diplomatic solution to the conflict between Israel and Hezbollah, the State Department said in a statement.

US envoy Amos Hochstein held talks with Lebanese officials in Beirut on Monday on conditions for a ceasefire between Israel and Hezbollah after Israel struck branches across Lebanon of a financial institution linked to the group.

He said that it was "not enough" for both sides to commit to UN resolution 1701, which ended the last round of conflict between Israel and the Lebanese militant group Hezbollah in 2006 and which calls for southern Lebanon to be free of any troops or weapons other than those of the Lebanese state.

Hochstein said that neither Hezbollah nor Israel had adequately implemented the resolution, and that while it would be the basis for the end to current hostilities, the US was seeking to determine what more needed to be done to make sure it was implemented "fairly, accurately and transparently."

"We are working with government of Lebanon, the state of Lebanon, as well as the government of Israel to get to a formula that brings an end to this conflict once and for all," he said.

Israel has pursued a ground campaign over the past month after a year of border clashes touched off by Hezbollah rocket fire into Israel in support of Hamas in Gaza.

The Israeli military said before its overnight attacks that it was targeting the Al-Qard Al-Hassan Association, a financial institution with over 30 outlets across Lebanon which the US has said is used by Hezbollah to manage its finances.

There was no immediate statement from the organisation, Hezbollah or the Lebanese government.

(The result of an Israeli airstrike in Beirut's southern suburbs in Lebanon. (AP PHOTO)

The ground outside the wrecked Al-Qard Al-Hassan branch in the city of Tyre was strewn with rubble, shattered glass and scattered papers.

At least two people were killed and three others injured on Monday in an apparent guided missile attack on a car in the heart of the Syrian capital, Damascus, Syrian state television said, quoting a military source who attributed the attack to Israel.

The Israeli military did not immediately comment.

Lebanon's health ministry on Monday said the death toll since Israel's offensive began had risen to 2483, with 11,628 injured.

Fifty-nine people have been killed in northern Israel and the occupied Golan Heights over the same period, say Israeli authorities.

Israel's campaign in Lebanon has driven 1.2 million people from their homes. It says its aim is to drive Hezbollah fighters from the border region so tens of thousands of Israelis can return to homes they were forced to flee over the past year due to Hezbollah cross-border fire in solidarity with Palestinians.

By Humeyra Pamuk and Timour Azhari in Washington/Beirut