The Israeli military has said that its planned operation in Gaza City would prevent Hamas fighters from regrouping and planning future attacks. Israel entered Gaza City earlier in the war, but said this time it would move into parts of the city that Israeli soldiers have not previously attacked or held.

The risks to civilians who leave — and those who stay — are enormous. Further intensification of military operations in Gaza City would cause a “catastrophe” for civilians, the United Nations Office for the Coordination of Humanitarian Affairs has warned.

Gaza City and the surrounding region are officially suffering from famine, the Integrated Food Security Phase Classification announced in August. The United Nations and aid agencies rely on the group, known as the I.P.C., to monitor and classify global hunger crises.

Photos and videos taken on Tuesday showed crowds of Palestinians heading south from Gaza City. Still, others said they planned to stay, saying the journey was too expensive, that they had nowhere to go, or that if they left, they feared they could never come back.

In its evacuation order for Gaza City, the Israeli military instructed people to go to what it called a “humanitarian zone” in the southern half of the territory, a thin coastal strip where hundreds of thousands of people have already taken refuge.

The Israeli military said there were “vast empty areas” that were “free of tents” there. But hundreds of thousands of Palestinians already live there, and parts of the zone overlap with areas the military has ordered evacuated.