Israeli forces have been carrying out an offensive on the suburbs of the northern city for weeks after Israeli Prime Minister Benjamin Netanyahu ordered the military to capture it.
Netanyahu says Gaza City is a Hamas stronghold and capturing it is necessary to defeat the Palestinian Islamist militants, whose October 2023 attack on Israel sparked the war.
The assault threatens to displace hundreds of thousands of Palestinians sheltering there from nearly two years of fighting. Before the war, around a million people, nearly half of Gaza's population, lived in the city.
Israeli military spokesman Avichay Adraee wrote on X that residents should leave the city for a designated coastal area of Khan Younis in southern Gaza, assuring those fleeing that they would be able to receive food, medical care and shelter there.
The designated area was a "humanitarian zone", Adraee said.
The military later bombed a high-rise Gaza City tower that it said was being used by Hamas, without providing evidence to support the assertion, and that civilians were warned in advance.
Israel's Defence Minister Israel Katz shared a video on X of what appeared to be the multi-storey building collapsing after the strike, sending a cloud of dust and debris into the air.
The Israeli military said Hamas used the building to gather intelligence and that explosive devices had been planted nearby.
Hamas denied using the building for military purposes, and Palestinians said it had been used to shelter the displaced.
Before the strike, Gazan health authorities reported at least 23 Palestinians had been killed on Saturday, including at least 13 in the Gaza City area.
The Israeli military bombed another high-rise tower on Friday that it had also said was being used by Hamas.
On Thursday, the military said it had control over almost half of Gaza City. It says it controls about 75 per cent of all of Gaza.
Many of those in Gaza City were displaced earlier in the war only to later return.
Some residents have said they refuse to be displaced again.
The military has been carrying out heavy strikes on the city for weeks, advancing through outer suburbs, and this week forces were within a few kilometres of the city centre.
Netanyahu, backed by right-wing coalition allies, ordered the capture of Gaza City against the advice of Israel's military leadership, according to Israeli officials.
The war in Gaza has increasingly left Israel diplomatically isolated, with some of its closest allies condemning the campaign that has devastated the small territory.
Palestinian militants took 251 hostages into the enclave after a Hamas-led cross-border attack on southern Israeli communities on October 7, 2023, that killed about 1200 people.
More than 64,000 Palestinians have since been killed in Gaza, local health authorities say, with much of the enclave reduced to ruins and its residents facing a humanitarian crisis.
There are also growing calls within Israel, led by families of hostages and their supporters, to end the war in a diplomatic deal that would secure the release of the remaining 48 captives, of whom 20 are believed to be alive.
Netanyahu is pushing for an all-or-nothing deal that would see all of the hostages released at once and Hamas surrendering.
Hamas has offered to release some hostages for a temporary ceasefire, similar to terms that were discussed in July before negotiations mediated by the US and Arab states collapsed.
Hamas, which has ruled Gaza for nearly two decades but today controls only parts of the enclave, has long said it would release all hostages if Israel agreed to end the war and to withdraw all its forces from Gaza.
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