Local health authorities said Israeli gunfire and strikes killed at least 30 people on Sunday, including 13 who tried to get food from near an aid site in the central Gaza Strip, and at least two in a house in Gaza City.
The Israeli military spokesperson's office said they were reviewing the reports.
Residents of Sheikh Radwan, one of the largest neighbourhoods of Gaza City, said the territory had been under Israeli tank shelling and air strikes throughout Saturday and on Sunday, forcing families to seek shelter in the western parts of the city.
The Israeli military has gradually escalated its operations around Gaza City in the past three weeks, and on Friday, it ended temporary pauses in the area that had allowed for aid deliveries, designating it a "dangerous combat zone".
"They are crawling into the heart of the city where hundreds of thousands are sheltering, from the east, north, and south, while bombing those areas from the air and ground to scare people to leave," said Rezik Salah, a father of two, from Sheikh Radwan.
An Israeli official said Netanyahu's security cabinet will convene on Sunday evening to discuss the next stages of the planned offensive to seize Gaza City, which he has described as Hamas's last bastion.
A full-scale offensive is not expected to start for weeks.
Israel says it wants to evacuate the civilian population before moving more ground forces in.
On Saturday, Red Cross head Mirjana Spoljaric said an evacuation from the city would provoke a massive population displacement that no other area in the Gaza Strip is equipped to absorb, amid severe shortages of food, shelter, and medical supplies.
"People who have relatives in the south left to stay with them. Others, including myself, didn't find a space as Deir Al-Balah and Mawasi are overcrowded," said Ghada, a mother of five from the city's Sabra neighbourhood.
About half of the enclave's more than two million people are presently in Gaza City.
Several thousand were estimated to have left the city for central and southern areas of the enclave, according to local sources.
Israel's military has warned its political leaders that the offensive is endangering hostages still being held by Hamas in Gaza.
Protests in Israel calling for an end to the war and the release of the hostages have intensified in the past few weeks.
Large crowds demonstrated in Tel Aviv on Saturday evening, and hostages' families protested outside the homes of ministers on Sunday morning.
The war began with a Hamas-led attack on southern Israel on October 7, 2023, in which about 1200 people were killed, mostly civilians, and 251 taken hostage.
Twenty of the remaining 48 hostages are believed to still be alive.
Israel's military campaign in Gaza has killed more than 63,000 people, mostly civilians, according to Gaza health officials, and it has plunged the enclave into a humanitarian crisis and left much of it in ruins.
On Sunday, the Gaza health ministry said seven more people had died of malnutrition and starvation in the enclave, raising the number of such deaths to 339 people, including 124 children, since the war began.
Israel disputes the fatality figures issued by the health ministry in the Hamas-run strip.
