Across the Gaza Strip, medics said a total of 47 people were killed on Saturday.
The Israeli military did not initially comment. The information provided by both sides cannot be independently verified.
The Israeli news portal ynet reported heavy bombing and a "ring of fire" in several parts of Gaza City, citing Palestinian sources.
According to information released by the Israeli military on Friday, around 480,000 Palestinians have already left the city, previously home to some 1 million people.
They are trying to make their way to al-Mawasi in the south-west of the territory, which Israel has designated as a "humanitarian zone."
The health authorities in the Gaza Strip put the number of Palestinians killed since the start of the war at more than 65,000. Although no distinction is made between civilians and combatants, most of the victims are believed to be civilians.
Displaced Palestinians traumatised by the advance say they have 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 the displaced 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 control Gaza City's eastern suburbs and in recent days have been pounding 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.
On Thursday, the Israel Defence Forces (IDF) said it believed 350,000 people had left Gaza City since the start of September and that about 600,000 remained.
Satellite imagery from September 18, reviewed by Reuters, shows new tents appearing in the areas south of Gaza City after September 5.
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 military had told Palestinians they could use the newly reopened Salah al Din road to escape to the south.
The IDF said an air strike had killed Mahmoud Yusuf Abu Alkhir, whom it identified as deputy head of military intelligence in Hamas' Bureij Battalion.
It said he had taken part in "terrorist attacks against Israeli troops and the state".
Hamas, the militant group administering the Gaza Strip, triggered the war when it attacked Israel on October 7, 2023, killing 1200 people and taking 251 back to the enclave as hostages, according to Israeli figures.
Families of the remaining 20 or so surviving hostages have been imploring Prime Minister Benjamin Netanyahu to stop the offensive and instead negotiate a ceasefire with Hamas to free their loved ones.
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 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.
