(AFP) - US Secretary of State Antony Blinken was in Israel Tuesday to push for a ceasefire in Gaza after his administration called for an end to the war in Lebanon "as soon as possible".

It is his 11th trip to the Middle East since Hamas's attack on Israel more than a year ago triggered the Gaza war, and his first since Israel's conflict with Hezbollah escalated late last month.

He is due to meet Prime Minister Benjamin Netanyahu and other top officials, as Israel weighs its response to Iran's October 1 missile attack.

In Lebanon, Israel hit an area of south Beirut housing the country's largest public health facility, killing 13 people, according to the health ministry.

The Rafic Hariri Hospital, located outside Hezbollah's traditional strongholds, sustained minor damage in the strike which flattened four buildings in its vicinity, said an AFP correspondent in the area.

Previous US efforts to end the Gaza war and contain the regional fallout have failed, as did a bid spearheaded by President Joe Biden and his French counterpart Emmanuel Macron to secure a temporary ceasefire in Lebanon.

After Israel, Blinken will visit Jordan on Wednesday and discuss humanitarian aid for the Gaza Strip, an official on the plane with him said.

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

- Night of strikes -

On Monday, US envoy to Lebanon Amos Hochstein said his administration was seeking an end to the war "as soon as possible" as he pushed for a ceasefire based on a UN resolution that had ended an earlier Israel-Hezbollah war.

Under resolution 1701, Hezbollah should have withdrawn from areas in south Lebanon near the Israeli border, leaving only the country's weak military and UN peacekeepers deployed there.

But Hezbollah remained south of Lebanon's Litani River, and in October last year began launching low-intensity cross-border strikes into Israel, in support of its Palestinian ally Hamas.

After nearly a year of war in Gaza, Israel shifted its focus to Lebanon, vowing to secure its northern border to allow tens of thousands of Israelis displaced by the cross-border fire to return to their homes.

Israel ramped up its air strikes on Hezbollah strongholds around the country and on September 30 sent in ground troops, in a war that has killed at least 1,489 people since September 23, according to an AFP tally of Lebanese health ministry figures.

The strike on Monday night came as Israel targeted Beirut's southern suburbs with heavy fire following evacuation warnings.

The densely populated Ouzai neighbourhood a few kilometres (miles) from the city centre was hit for the first time in the conflict, sparking an exodus of residents.

The Israeli military said it was targeting Hezbollah's naval unit, and that it had issued an evacuation warning.

A Lebanese security official told AFP that the country's national airline had to switch landing strips after Israeli strikes near Beirut's only international airport hit close to the main runway.

Hezbollah on Tuesday said it launched rockets targeting two positions in the suburbs of Israel's commercial hub Tel Aviv, including an intelligence base.

It also said it targeted Israel's "Stella Maris naval base" near the northern city of Haifa, and that its militants had clashed with Israeli troops near a village at the border.

In a war-hit area along the Lebanese border, AFP footage showed huge clouds of smoke rising following Israeli strikes on the village of Khiam, as trails of smoke from Hezbollah rockets fired towards Israel could also be seen.

The wars in Gaza and Lebanon have also drawn in other Iran-aligned armed groups, including in Yemen, Syria and Iraq.

Iran on Tuesday said it had received assurances from its neighbours that they would not allow the use of their airspace for any attack against it, after Israel pledged to hit back against its October 1 missile attack.

- 'We will die of hunger' -

In the Gaza Strip, Israel launched a major air and ground assault in northern Gaza earlier this month, vowing to stop Hamas militants from regrouping in the area.

Gaza's civil defence agency said four Palestinians were killed in strikes on Monday, while several homes were blown up in the northern area of Jabalia, a focal point of the recent fighting.

A displaced resident said Jabalia "is being wiped out".

"If we don't die from the bombing and gunfire, we will die of hunger," said 42-year-old Umm Firas Shamiyah, demanding aid be sent to the north.

Tens of thousands of people are estimated to have fled the assault on northern Gaza, and according to the UN agency for Palestinian refugees around 400,000 people were trapped in the area last week.

The UN has warned of the risk of famine in Gaza, its figures showing that 396 aid trucks have entered the territory so far this month -- far below the 3,003 seen in September.

The war was sparked by Hamas's unprecedented attack on Israel on October 7 last year, which resulted in the deaths of 1,206 people, mostly civilians, according to an AFP tally of official Israeli figures.

Israel's offensive in Gaza has killed 42,718 people, a majority civilians, according to data from the health ministry in the Hamas-run territory, figures the UN considers reliable.

© Agence France-Presse