Prime Minister Benjamin Netanyahu vowed Monday that Israel will take control of "overall security" of besieged Gaza after the war, as the Hamas-run health ministry said the death toll has surged past 10,000.

Resisting calls for a ceasefire, Netanyahu said there would be no letup in the war to destroy Hamas, whose October 7 attack left 1,400 dead in Israel, most of them civilians.

Hamas also took more than 240 people hostage, including children and elderly people, in an attack that prompted Israel's massive bombardment of Gaza and an intensifying ground offensive.

One month since the war began, the Hamas-run health ministry said the death toll in Gaza had surpassed 10,000 people — more than 4,000 of them children.

With international criticism of Israel's conduct of the war mounting, UN Secretary-General Antonio Guterres said Gaza was becoming a "graveyard for children".

More than 1.5 million people in densely packed Gaza have fled their homes for other parts of the territory in a desperate search for cover, with critical aid only trickling in.

But Netanyahu told ABC News the war would continue until Israel had restored "overall security" control of Gaza.

"Israel will, for an indefinite period, will have the overall security responsibility," he said.

"When we don't have that security responsibility, what we have is the eruption of Hamas terror on a scale that we couldn't imagine."

' Significant strikes'

Netanyahu's comments came after the White House said the Israeli leader had discussed potential "tactical pauses" in a phone call with US President Joe Biden on Monday.

But no agreements were announced and the pair did not broach the possibility of a ceasefire.

While key Israeli ally the United States is seeking a humanitarian "pause" in the fighting, several countries and UN agencies have repeatedly called for a ceasefire.

"There will be no ceasefire — general ceasefire — in Gaza, without the release of our hostages," Netanyahu said. 

"As far as tactical, little pauses — an hour here, an hour there — we've had them before. I suppose we'll check the circumstances in order to enable goods — humanitarian goods — to come in or our hostages, individual hostages, to leave," he added.

The Israeli army said it had pounded Gaza with "significant" strikes on 450 targets over 24 hours since Sunday morning, and that troops were targeting Hamas commanders in underground tunnels.

Israeli infantry and tanks have flooded the northern half of the Gaza Strip and tightened an encirclement of Gaza City, effectively splitting the territory in two.

Israeli troops who have taken up positions near the Gaza border told AFP they felt proud to protect their country but also nervous as the war intensifies.

Stationed near Gaza, a 20-year-old soldier said he was "a bit scared to go" into the Palestinian territory if given the order.

"You don't know if you can come back alive," said the soldier, whose name like those of other troops cannot be published because of Israeli military censorship.

Around 30 Israeli soldiers have been killed in the offensive, the latest on Monday, according to a report from the UN Office for the Coordination of Humanitarian Affairs, citing Israeli sources.

Statue of Liberty protest

Israel withdrew its troops from the Gaza Strip in 2005. A year later, Hamas won elections in Gaza, and subsequently seized control of the territory in 2007.

The Fatah party of Palestinian president Mahmud Abbas, which dominates the Palestinian Authority, only exercises limited autonomy in parts of the occupied West Bank.

US Secretary of State Antony Blinken suggested last week that the Palestinian Authority should retake control of Gaza after the war, and visited the West Bank to meet Abbas on Sunday.

But Hamas said they would never accept a puppet government in Gaza and that "no force on Earth could annihilate" it, said senior Hamas official in Lebanon, Osama Hamdan.

Blinken on Tuesday concluded his latest whirlwind Middle East tour, landing in Japan for a meeting of G7 foreign ministers set to seek a common line on Gaza.

The United States has bolstered its forces in the region, deploying two carrier strike groups and other assets to drive home its message that regional actors should not seek to take advantage of the conflict.

Hamas fired 16 rockets from Lebanon towards northern Israel on Monday, while Yemen's Iran-backed Huthi rebels claimed they had launched a fresh drone attack against Israel.

The Pentagon said Monday a US nuclear-powered Ohio-class submarine was in the Middle East to help prevent war from widening.

Meanwhile, in the latest protest, hundreds of US Jewish activists peacefully occupied New York's Statue of Liberty on Monday to demand a ceasefire an end to the "genocidal bombardment" of civilians in Gaza.

"As long as the people of Gaza are screaming, we need to yell louder, no matter who attempts to silence us," said photographer Nan Goldin at the protest.

Overnight 'massacres'

According to the Hamas-run health ministry, Israel's latest overnight barrage killed 292 people and hit two paediatric hospitals and Gaza's only psychiatric hospital.

"These are massacres! They destroyed three houses over the heads of their inhabitants — women and children," Mahmud Meshmesh, a resident of Deir al-Balah in central Gaza, told AFP.

"We have already taken 40 bodies out of the rubble," he said as crowds prayed around corpses wrapped in white shrouds.

Israeli officials accuse Hamas of building tunnels underneath hospitals, schools and places of worship in Gaza to hide fighters, store arms and ammunition, and plan attacks — charges the militant group has denied.

Israel has air-dropped leaflets and sent text messages ordering Palestinian civilians in northern Gaza to head south. A US official said Saturday at least 350,000 civilians remained in the worst-hit areas.

The Rafah crossing between the Gaza Strip and Egypt reopened Monday to allow the evacuation of foreigners and dual nationals, the Hamas government said, ending a two-day closure prompted by a dispute over the passage of ambulances.

On Monday, 93 aid trucks carrying food, medicine and water crossed from Egypt into Gaza, the United Nations said, but the needs are overwhelming.

A convoy including four ambulances arrived in Egypt via the Rafah crossing on Monday, the International Committee of the Red Cross said. 

"I have lost my home and have nothing left. I came here with nothing but the clothes I'm wearing," said Dana Okal, a Swedish passport holder.