Residents of Gaza struggled Saturday to flee from areas of the strip targeted by the Israeli military while grappling with a growing water crisis after Israel stopped the flow of resources to the region ahead of an expected land offensive a week after Hamas’ attack on Israel.

Israel, in line with its long-standing policy to minimize non-military casualties, renewed calls on social media and in leaflets dropped from the air for Gaza residents to move south, while Hamas, which has a long-standing record of hiding behind non-combatants,  urged people to stay in their homes.

The United Nations and aid groups have said such a rapid exodus would cause human suffering for hospitalized patients, older adults and others unable to relocate. It did not address the countervailing risk of civilians staying put as the hunt for Hamas’s leaders and infrastructure gets underway.

The evacuation directive covers an area of 1.1 million residents, or about half of the territory’s population. The Israeli military said “hundreds of thousands” of Palestinian Arabs had already heeded the warning and headed south. It said Palestinian Arabs could travel within Gaza without being harmed along two main routes from 10 a.m. to 4 p.m. local time.

It was not clear how many Palestinian Arabs remained in north Gaza by Saturday afternoon, said a spokeswoman for the UN’s agency for Palestinian Arab refugees,  Juliette Touma. “What we know is that hundreds of thousands of people have fled. And that 1 million people have been displaced in total in one week,” she said.

Families in cars, trucks, and donkey carts packed with possessions crowded a main road heading away from Gaza City as Israeli airstrikes continued to hammer the 25-mile-long territory, where supplies of food, fuel and drinking water were running low because of a complete Israeli siege.

Water has stopped coming out of taps across the territory. Amal Abu Yahia, a 25-year-old pregnant mother in the Jabaliya refugee camp, said she waits anxiously for the few minutes each day or every other day when contaminated water trickles from the pipes in her basement. She then rations it, prioritizing her five-year-old son and three-year-old daughter. 

Near the coast, the only tap water is contaminated with Mediterranean Sea water because of the lack of sanitation facilities. Mohammed Ibrahim, 28, said his neighbors in Gaza City have taken to drinking the salt water.

The Israeli military’s evacuation would force the territory’s entire population to cram into the southern half of the Gaza Strip as Israel continues strikes across the territory, including in the south.

Rami Swailem said he and at least five families in his building decided to stay put in his apartment near Gaza City. “We are rooted in our lands,” he said. “We prefer to die in dignity and face our destiny.”

Others were looking desperately for ways to evacuate. “We need a number for drivers from Gaza to the south, it is necessary #help,” read a post on social media. Another person wrote: “We need a bus number, office, or any means of transport,” posted another.

The UN refugee agency for Palestinians expressed concern for those who could not leave their current locations, “particularly pregnant women, children, older persons and persons with disabilities,” saying they must be protected. The agency also called for Israel to not target civilians, hospitals, schools, clinics and UN locations, though they are often sites where Hamas hides its personnel.

An Israeli military spokesman, Jonathan Conricus, said the evacuation was aimed at keeping civilians safe and preventing Hamas from using them as human shields. He urged persons in the targeted areas to leave immediately and to return “only when we tell them that it is safe to do so.”

“The Palestinian civilians in Gaza are not our enemies. We don’t assess them as such, and we don’t target them as such,” Mr. Conricus said. “We are trying to do the right thing.”

Thousands of people crammed into a UN-run school-turned-shelter in Deir al-Balah, a farming town south of the evacuation zone. Many slept outside on the ground without mattresses, or in chairs pulled from classrooms.

“I came here with my children. We slept on the ground. We don’t have a mattress, or clothes,” Howeida al-Zaaneen, 63, who is from the northern town of Beit Hanoun, said. “I want to go back to my home, even if it is destroyed.”

The Israeli military said its troops conducted temporary raids into Gaza on Friday to battle terrorists and hunted for traces of some 150 people — including men, women and children — who were abducted during Hamas’ assault on southern Israel.

The Hamas-aligned Gaza Health Ministry claimed Saturday that over 2,200 people have been killed in the territory, including 724 children and 458 women. The assault by Hamas has killed more than 1,300 people on the Israeli side, most of them civilians, and roughly 1,500 Hamas militants were killed during the fighting, the Israeli government said.

Egyptian officials said the southern Rafah crossing would open later Saturday for the first time in days to allow foreigners out. One official said both Israel and Palestinian militant groups had agreed to facilitate the departures and that talks were still underway about getting aid into Gaza through the same crossing. The officials were not authorized to brief journalists and spoke on condition of anonymity.

Fearing a mass exodus of Palestinians, Egyptian authorities erected “temporary” blast walls on Egypt’s side of the crossing, which has been closed for days because of Israeli airstrikes, two Egyptian officials said on condition of anonymity because they were not authorized to brief the press.

Israel’s raids into Gaza on Friday were the first acknowledgment that Israeli troops had entered the territory since the military began its round-the-clock bombardment following the massacre by Hamas. Palestinian Arab terrorists have fired more than 5,500 rockets into Israel since the fighting erupted, the Israeli military said.

Israel has called up some 360,000 military reserves and massed troops and tanks along the border with Gaza. A ground assault in densely populated Gaza could bring even higher casualties on both sides in house-to-house fighting.

At Riyadh, Secretary Blinken met Saturday with the Saudi Arabian foreign minister, Faisal bin Farhan, and both called for Israel to protect civilians in Gaza. Israel has made it a policy to minimize civilian casualties in all its battles in the district — and elsewhere.

“As Israel pursues its legitimate right to defend its people and to try to ensure that this never happens again, it is vitally important that all of us look out for civilians, and we’re working together to do exactly that,” Mr. Blinken said.

Mr. Blinken’s comment in Saudi Arabia was in sharp contrast to that of the American defense secretary, Lloyd Austin, himself a combat veteran. Mr. Austin, as our Benny Avni reported,  said this week that he trusts the IDF as a “professional force,” and that he shared his own experience in fighting terrorism while also learning from the Israelis. 

Hamas claimed Israel’s airstrikes killed 22 hostages, including foreigners. It did not provide their nationalities. The Israeli military denied the claim. Hamas and other Palestinian Arab terrorists apparently hope to trade the hostages for thousands of Palestinian Arabs held in Israeli prisons.

At the West Bank, the Palestinian Arab Health Ministry says that 53 Palestinians Arabs have been killed since the start of the war, including 16 on Friday. The United Nations says attacks by Israeli settlers have surged there since the assault by Hamas.

America and Israel’s other allies have pledged support for the war on Hamas. The European Union’s foreign policy chief, however, said Saturday that the Israeli military needed to give people more time to leave northern Gaza.

Josep Borrell welcomed the evacuation order but said, “You cannot move such a volume of people in (a) short period of time,” noting a lack of shelters and transportation.

Patients and personnel from the Al Awda Hospital in Gaza’s far north spent part of their night in the street “with bombs landing in close proximity,” the medical aid group Doctors Without Borders said. A spokesman for the group, Scott Hamilton, said some of the medical staff and all patients were moved to another location, “but the situation remains extremely complicated and chaotic.”