Gaza City, in the north of the Palestinian enclave, was one of the first areas that Israeli troops moved into at the start of the war.
But fighting with militants still holding out there has persisted and civilians have sought shelter elsewhere, adding to multiple waves of displacement.
Much of the city lies in ruins.
Residents said neighbourhoods in Gaza City had been bombed throughout the night and into the early morning hours.
Several multi-storey buildings had been destroyed, they said.
The Gaza Civil Emergency Service said it believed dozens of people were killed but emergency teams were unable to reach them because of ongoing offensives in Daraj and Tuffah in the east and Tel al-Hawa, Sabra and Rimal further west.
Gaza residents said tanks advanced from at least three directions on Monday and reached the heart of Gaza City, backed by heavy Israeli fire from the air and ground.
That forced thousands of people out of their homes to look for safer shelter, which for many was impossible to find. Some slept on the roadside.
One tank thrust pushed people towards the western road near the Mediterranean, residents said.
“While the Hamas movement demonstrates flexibility and positivity to facilitate reaching an agreement to halt the Zionist aggression, Netanyahu is placing additional obstacles in the way of negotiations as he escalates his aggression and crimes against our people,” the militant group said.
Hamas on Saturday accepted a key part of a US plan aimed at ending the nine-month war in Gaza, dropping a demand that Israel first commit to a permanent ceasefire before signing the agreement.
A US delegation led by Central Intelligence Agency director William Burns arrived in Cairo on Monday to meet an Egyptian security delegation for a new round of ceasefire talks, the Egyptian state-affiliated al-Qahera News reported.
The war was triggered on October 7 when fighters led by Hamas, which controlled Gaza, attacked southern Israel, killing 1200 people and taking about 250 hostages, according to Israeli figures.
Since then at least 38,193 Palestinians have been killed in the military offensive and 87,903 have been wounded, Gaza’s health ministry said in an update on Monday.
Israel’s military said on Monday it was close to finishing its operational investigation into the handling of Hamas’ October attack.
It said the findings will first be presented to the communities along the border with Gaza that were attacked and the families of hostages being held in Gaza.
After that, they will be made public.
