Israel escalated its offensive on Wednesday to seize Gaza City, and ordered all residents to leave, while Hamas continued to review US President Donald Trump's ceasefire plan.
The Israel Defense Forces said troops began precise ground activity to boost control of a key strategic "corridor."
Israeli Defense Minister Israel Katz said in a post on social media that the country is "tightening the siege" around Gaza City to defeat Hamas.
He warned its residents that this is the "last chance" for them to move south, and those who remain will be considered "terrorists and supporters of terror."
Katz also stressed the IDF will not stop operations, until all the hostages are returned and Hamas disarms.
Hamas condemned Katz's announcement. The group issued a statement, saying this will "pave the way for an escalation of the war crimes" against people in the city.
IDF Radio said on Saturday about 780,000 people have evacuated, but approximately 250,000 remain.
Trump announced his 20-point ceasefire plan after meeting with Israeli Prime Minister Benjamin Netanyahu at the White House on Monday. Netanyahu said he would support the plan, and Hamas promised they would study it.
The plan says that if both sides agree to the proposal, "the war will immediately end." It also says that all military operations will be suspended.
The plan also stipulates that Hamas must return all the hostages, living and dead, within 72 hours after Israel publicly accepts the agreement.
White House Press Secretary Karoline Leavitt commented on the progress with Hamas at a news conference. She said "there are some very sensitive discussions that are taking place." But she did not provide any details.

Quiz 1:
What did Israel Defense Forces start doing on Wednesday to boost control in Gaza City?
A. Ground activities to seize a key strategic corridor
B. Air strikes against various targets
C. Naval blockade of the Gaza Strip
D. Negotiations with Hamas for a ceasefire

Quiz 2:
Who issued a statement condemning Israeli Defense Minister Israel Katz's announcement?
A. The United Nations Security Council
B. Palestinian Authority President Mahmoud Abbas
C. White House Press Secretary Karoline Leavitt
D. Hamas, the de facto governing power in Gaza

Quiz 3:
What will happen according to Donald Trump's ceasefire plan if both sides agree to it?
A. The hostages will be returned and Hamas will disarm within 72 hours
B. A new round of negotiations between Israel and Palestine will start
C. The US military will intervene in the conflict
D. An immediate peace treaty will be signed by both parties