Israeli air strikes pounded Gaza City on 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 on Wednesday his forces were "tightening the stranglehold" around Gaza City, as they pressed an offensive launched after the Hamas attacks on October 7 that killed 1,400 people in Israel, mainly civilians.

The militants also took more than 240 people hostage.

Vowing to destroy Hamas, Israel has conducted relentless bombardments that the
health ministry in Gaza says has killed more than 10,500 people, many of them children.

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

In a 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.

He said there would be no ceasefire unless the hostages held in Gaza are released. (AFP)