Israeli air strikes pounded Gaza City Thursday as soldiers battled street-by-street with Hamas militants, and tens of thousands of Palestinians desperate for safety fled their homes southwards in the besieged territory.

After more than a month of intense bombardment, hundreds of thousands of people remain trapped in a "dire humanitarian situation" in battle zones without enough food and water, the United Nations said.

Israeli Defence Minister Yoav Gallant said Wednesday his forces were "tightening the stranglehold" around Gaza City, as they pressed an offensive launched in response to the Hamas attacks on October 7 that killed 1,400 people in Israel, mainly civilians.

The militants also took more than 240 people hostage, among them babies and elderly people.

Vowing to destroy Hamas, Israel retaliated with a relentless bombardment and ground invasion that the Hamas-run health ministry in Gaza says has killed more than 10,500 people, many of them children.

- 'Where can we go?' -

"We've lost our homes, we've lost our children. Where is the global community?" said Nouh Hammouda, who was among those fleeing.

"We left our homes due to the relentless bombardment. Where can we go now?" Hammouda added, as people streamed southwards.

In the Indonesian hospital in Beit Lahia, in the northern Gaza Strip, a weeping father cradled the body of his two-year-old son Mohammed Abu Qamar, who died after an air strike.

"Please don't put him in the morgue, let me take him home and I will bury him tomorrow", his father Nidal said, as his wife screamed in grief alongside him.

Israeli Prime Minister Benjamin Netanyahu has repeatedly rejected the prospect of a ceasefire in Gaza. 

On Wednesday, he reiterated his refusal, saying there would be no ceasefire unless the hostages held in Gaza are released. 

According to a source close to Hamas, talks are underway for the release of a dozen hostages, including six Americans, in return for a three-day ceasefire.

The United States has backed Israel's rejection of a ceasefire, and G7 foreign ministers on Wednesday in Japan said they supported "humanitarian pauses and corridors" in the war.

Israel has set an aim of destroying Hamas, with its soldiers targeting their deep network of tunnels and underground bases, while air-dropping leaflets and sending text messages ordering civilians in northern Gaza to flee south.

The army said 50,000 people had fled their homes in the main battle zone of northern Gaza on Wednesday, a sharp increase in numbers from earlier this week, adding to the more than 1.5 million people already seeking safety in the south of the coastal strip.

"They're leaving because they understand that Hamas lost control in the north, and in the south it's safer", Israeli military spokesman Daniel Hagari said.

The UN Office for the Coordination of Humanitarian Affairs (OCHA) confirmed the figure, and warned that conditions were "dire" in battle zones north of the central Wadi Gaza district.

"Hundreds of thousands of people remaining north of Wadi Gaza, including IDPs (internally displaced people), are facing a dire humanitarian situation and are struggling to secure the minimum amounts of water and food to survive."

- 'Collective punishment' -

UN rights chief Volker Turk condemned Israel over its bombardment and its orders to Gazans to flee southwards.

"The collective punishment by Israel of Palestinian civilians amounts also to a war crime, as does the unlawful forcible evacuation of civilians," he told reporters at the Rafah border crossing with Egypt, the only way route out of Gaza not controlled by Israel.

More than 100 trucks carrying aid crossed into Gaza from Egypt on Wednesday, OCHA said, taking the total to 756 since fighting began last month, less than what would normally have entered Gaza in just two days before the war.

"The aid getting through is a trickle," Turk said.

A rare delivery of emergency medical supplies reached Gaza City's main Al-Shifa hospital on Wednesday, just the second since the war began, the UN and World Health Organization said, warning it "far from sufficient to respond to the immense needs".

Tom Potokar, chief surgeon at the International Committee of the Red Cross, described the scene at the European hospital in Khan Yunis in southern Gaza as "catastrophic". 

"In the last 24 hours, I've seen three patients with maggots in their wounds," including a six-year-old child, he said by telephone, reporting children were coming into the hospital who have "lost their whole family."

- 'Revenge' -

Images taken by an AFP journalist embedded with Israeli troops showed them emerging from tanks to comb the shells of Gaza residential buildings destroyed in the past month.

"You feel like the whole of Israel is behind you," said Ben,a 24-year-old Israeli combat engineer inside Gaza, who like all soldiers, cannot be fully named published because of military censorship.

"It feels amazing that you're the one that takes care of what happened after October 7, you're kind of giving the revenge after what they did."

The Israeli government said Wednesday it was "premature" to predict scenarios for Gaza once it ousts Hamas, but that it was already discussing the prospect with other countries.

Netanyahu earlier this week said that Israel would assume "overall security" of Gaza.

Israel withdrew from the Gaza Strip in 2005 and two years later imposed a crippling air, sea and land blockade when Hamas took control of the Palestinian territory.

US National Security Council spokesman John Kirby told reporters on Wednesday that it was plausible that "for at least some period of time" Israeli forces would remain in Gaza "to manage the immediate aftermath and security situation".

Senior Hamas member Ezzat al-Reshq gave short shrift to the suggestions.

"All the powers of the world together would not be able to impose its conditions or its puppets" on the Palestinians, he wrote in a message on Telegram.

Efforts continue to allow access for people to leave Gaza.

A Hamas official told AFP that evacuations of wounded Palestinians and dual nationals were interrupted Wednesday, blaming what the group said was Israel's refusal to approve the list of wounded to be taken across the border.

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