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, about a million people - nearly half of the enclave'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 also issued so-called "evacuation warnings" to civilians in certain areas of the city, warning it was about to carry out attacks.
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.
It said civilians were warned in advance.
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 the Gaza Strip.
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 local health authorities in the Gaza Strip 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.
Israeli officials believe 20 of the hostages are alive.
US President Donald Trump said on Friday that his officials were in "very deep" negotiations with the Palestinian militants.
Hamas, which has ruled the Gaza Strip 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 the the strip.
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