Taking over the city of one million Palestinians complicates ceasefire efforts to end the nearly two-year war as Prime Minister Benjamin Netanyahu and his far-right partners follow through with his plan to take on what they have said are Hamas's two remaining strongholds.
The evacuation orders caused panic and confusion among the residents of Gaza City.
Some said they would have no choice but to leave for the south, while the vast majority of others said they would stay as no other place was safe.
Netanyahu warned residents of Gaza City to leave now, saying forces were organising and assembling into Gaza City for a ground "manoeuvre".
"I say to the residents of Gaza, take this opportunity and listen to me carefully: you have been warned - leave now!" Netanyahu said.
Hopes were pinned on mediation efforts to reach a ceasefire that would avert Israel's plan to take control of the enclave's largest urban city.
Qatar has been pressing Hamas leaders to "respond positively" to the latest US-proposed Gaza ceasefire-hostage deal during talks in Doha on Monday, an official briefed on the talks told Reuters.
Hamas said it received some ideas from the United States' side to reach a ceasefire deal in Gaza, and was discussing with mediators ways to develop those ideas.
Israel had accepted a Gaza ceasefire proposal from US President Donald Trump, Israeli Foreign Minister Gideon Saar said on Monday.
International critics say Israel's plan, which includes demilitarising the whole strip as Israel takes security control of it, could deepen the humanitarian plight of the 2.2 million population, which faces a critical risk of famine.
Netanyahu had said Israel had no choice but to complete the job and defeat Hamas, given the Palestinian militant group had refused to lay down its arms.
Hamas said it would not disarm unless an independent Palestinian state was established.
Israel had already taken control of 75 per cent of Gaza since the war began with Hamas's cross-border assault on October 7, 2023, in which some 1200 people were killed and 251 taken hostage, Israeli tallies show.
Israeli authorities say 20 of the remaining 48 hostages in Gaza are alive.
Israel's subsequent military assault has killed more than 62,000 Palestinians, Gaza's health ministry says, and internally displaced nearly the entire population and left much of the territory in ruins.
