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Lebanon's health ministry on Tuesday said 13 people, including a child, were killed in an Israeli strike near a south Beirut hospital the previous night, revising upwards its initial toll of four.

Another 57 people were wounded in the strike near Lebanon's biggest public hospital, located a few kilometres from the city centre, the health ministry said.

Earlier, Lebanon's Hizbollah group said it targeted on Tuesday two positions in the suburbs of Israel's commercial hub Tel Aviv, including an intelligence base for the second time in a few hours.

A "salvo of rockets" was fired against the "Glilot base of the 8200 military intelligence unit", the Iran-backed group said in a statement, after having claimed on Monday night similar attacks on the same position. Also Tuesday, the group said it fired rockets at another position in Tel Aviv's suburbs.

The Israeli military said five projectiles were fired from Lebanon into Israel and said most were intercepted by Israel's missile defence system. One landed in an open area.

The rocket fire came as Israel stepped up its strikes in Lebanon, targeting a Hizbollah-run financial institution, and as the US pushed to resume cease-fire talks in Gaza following the death of Hamas leader Yahya Sinwar.

Israeli Prime Minister Benjamin 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 cease-fire, a full Israeli withdrawal from Gaza and the release of Palestinian prisoners.

Hamas-led blew holes in Israel's security fence and stormed in, killing some 1,200 people, mostly civilians, and abducting another 250.

Israel's offensive in Gaza has killed over 42,000 Palestinians, according to local health authorities, who do not distinguish combatants from civilians.

The war has destroyed large areas of Gaza and displaced about 90% of its population of 2.3 million people.

Israel strikes 300 Hizbollah targets

Israel said on Monday it struck around 300 Hizbollah targets in Lebanon over 24 hours, ramping up its offensive to hit the group's finances, as the United States called for the war to end "as soon as possible".

This picture shows a damaged building at the site of Israeli airstrike in the city of Tyre, Lebanon, on Monday. AFP

US Secretary of State Antony Blinken is due to begin a tour of the Middle East in Israel on Tuesday in a new push for an elusive ceasefire in the Gaza Strip after more than a year of war there and to contain the regional escalation.

In Lebanon, the health ministry said four people were killed and 24 wounded Monday evening in Israeli strikes near the country's largest public hospital, in the southern suburbs of the capital Beirut.

'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 fighters 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 focus 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 northern Gaza 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.

In Gaza, 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 42,603 people, a majority civilians, according to data from the health ministry in the Hamas-run territory, figures the UN considers reliable.