Israel's military said it had expanded attacks on Gaza City while displaced Palestinians traumatised by the advance said they had no means to flee.
"The situation is really bad. All night long, the tank was firing shells," said Toufic Abu Mouawad, who left a camp for displaced people with nowhere else to go.
"I want to flee with the boys, the girls, the children. This is the situation that we are living in. It is a very tragic situation. We call on all the Arab countries and the people who have a good conscience to stand with us."
Israeli forces advance on central Gaza City
Israeli forces control Gaza City's eastern suburbs and in recent days have been bombing the Sheikh Radwan and Tel Al-Hawa areas, from where they would be positioned to advance on central and western areas, where most of the population is sheltering.
The Gaza health authorities said 33 Palestinians had been killed by Israel in the last 24 hours.
The Israel Defence Forces (IDF) claimed yesterday that around 350,000 people had left Gaza City since the start of September and that about 600,000 remained.
Satellite imagery from 18 September, reviewed by Reuters, shows new tents appearing in the areas south of Gaza City after 5 September.
It also shows crowds of people on the Al Rashid Road and what appear to be vehicles on the Salah al Din Road.
In leaflets dropped over Gaza City, the IDF told Palestinians they could use the reopened Salah al Din Road to escape to the south from their attacks.
The IDF said an airstrike had killed Mahmoud Yusuf Abu Alkhir, whom it claimed was deputy head of military intelligence in Hamas' Bureij Battalion.
It also claimed he had taken part in "terrorist attacks against Israeli troops and the state".
Families of the remaining 20 or so surviving hostages have been imploring Netanyahu to stop the offensive and instead negotiate a ceasefire with Hamas to free their loved ones.
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Israeli protesters call for hostage releases
Dozens of protesters gathered on the Israeli side of the border, calling for an end to the war.
They held banners or placards with slogans that included "Stop the genocide in Gaza" and "Free Gaza, isolate Israel".
The armed wing of Hamas said yesterday that the hostages were distributed throughout the neighbourhoods of Gaza City.
"The start of this criminal operation and its expansion means you will not receive any captive, alive or dead," it said in a written statement.
Israel Katz, Israel's defence minister, said on X, formerly Twitter: "If Hamas does not release the hostages and disarm, Gaza will be destroyed and turned into a monument to the rapists and murderers of Hamas."
In almost two years, Israel's war has killed more than 65,000 Palestinians, according to Gaza health authorities, and demolished most of the structures in the tiny enclave, which is now gripped by famine over Israel’s blockade.
Israel claims the extent of hunger has been exaggerated and that Hamas could end the war at once if it surrendered, freed the hostages, disarmed and disbanded.
Hamas said it will not disarm until a Palestinian state is established.
Numerous attempts to mediate an end to the conflict have failed.
Displaced Palestinian Osama Awad said the Israeli attacks were coming closer: "For one week, we have been living nights of horror."
It is a horror that most of Gaza's 2 million Palestinians have experienced over and over again in repeated Israeli onslaughts and multiple displacements.
All around Mr Awad, children sat on top of piles of their families' meagre belongings while others moved a few possessions on carts.
