The pattern has repeated itself across the territory, as critics say Israel has done little to fill the power vacuum left behind when its troops move on. The latest raid was coupled with evacuation orders for several neighborhoods in the city and areas west of it, and crowds of people were scrambling to get out.

Zainab al-Khaldi, a lawyer and researcher with UNICEF who was working at a school-turned-shelter in Al-Daraj, one of the areas that the Israeli military moved into on Monday, described a frantic effort to figure out which way to go after the shelter where she was staying came under artillery fire with no warning on Monday evening.

“People went crazy and started running in all directions,” she said in a phone interview. Ms. al-Khaldi said she saw more than 20 people who were wounded by the shelling, “and no one could reach them to help.”

The military was already conducting a separate operation in the city, in the Shajaiye neighborhood in the east, which entered its 12th day on Tuesday. The Israeli military said it was “engaged in close-quarters combat” above and below ground with Palestinian militants. It said it had killed more than 150 militants in Shajaiye and “located tunnel shafts and significant tunnel routes.” The United Nations office of humanitarian affairs said 60,000 to 80,000 people were displaced on the first night of that raid.

About 20 minutes after the shelter in Al-Daraj was hit, Ms. al-Khaldi said she and others there started getting text messages and automated phone calls from the Israeli military instructing them to evacuate to the west. People started to do so, but many felt trapped as fighting raged in several areas nearby.

“If we wanted to go east to Shajaiye, there’s bombing,” she said. “If we wanted to go toward Al-Ahli Hospital there’s bombing,” describing a facility where people have been sheltering in central Gaza City.

“There was danger in all places,” she said.

Ms. al-Khaldi and a crowd of others headed west “under an insane amount of fire from quadcopters,” she said, before she was able to find shelter in the home of some she knows.

“This was not our first displacement and it will not be our last,” she said.

Humanitarian groups have condemned the new Israeli incursions and evacuation orders. The U.N. Human Rights Office said in a statement on Monday that it was “appalled” by the orders issued to Gaza City residents, “many of whom have been forcibly displaced multiple times.” It said the orders were confusing and often told people to move to combat areas.

The main U.N. agency that assists Palestinian refugees, known as UNRWA, said in a post on X that the displacements meant that “people have to move back to destroyed areas despite the threat of unexploded ordnance.”

Wafa, the Palestinian Authority’s official news agency, reported that dozens of Palestinians were killed and wounded in the neighborhoods of Al-Daraj, Al-Tuffah and the Old City amid intense Israeli bombardment. The agency added that Israeli attacks had also targeted Deir al Balah, an area in central Gaza where many of those fleeing had headed.

The Palestinian Red Crescent said in a statement that all of its smaller clinics and emergency rooms in Gaza City were “out of service” because they were located in the evacuation zones.

Rawan Sheikh Ahmad contributed reporting.

To evade Israeli inspections, smugglers — mostly in Egypt — have been hiding them in sacks of United Nations-donated flour, diapers and even a watermelon, according to aid agencies and an Israeli military official who shared photos with The New York Times.

Aid trucks that set off from the crossing into Gaza were then attacked by crowds of Palestinians, some of them armed, seeking the cigarettes hidden inside, according to U.N. and Israeli officials.

Andrea De Domenico, who runs the U.N. Office for the Coordination of Humanitarian Affairs in Jerusalem, confirmed that aid officials had “seen cartons of U.N.-branded assistance with cigarettes inside.” He said the contraband cigarettes had created “a new dynamic” of organized attacks on aid convoys.

Israel’s near-total control of the goods that enter Gaza amid the war has warped the enclave’s economy. The price of flour has plunged in parts of Gaza because Israel, under intense international pressure to ease hunger, has allowed aid agencies to pump in large amounts of it. Other commodities, which have entered less frequently, remain rarer and more expensive.

Mr. De Domenico showed The Times footage he had taken during a recent drive along the road leading into Gaza from Kerem Shalom: Full flour bags can be seen strewed along the side of the road, seemingly of little interest to the looters.

“Their main purpose here was to search for the cigarettes,” said Manhal Shaibar, who runs a Palestinian trucking company at Kerem Shalom that ferries U.N. aid.

Officials said that most of the trucks bearing cigarettes appeared to come from Egypt, which rerouted trucks arriving from Egyptian territory through Kerem Shalom after Israel captured the Rafah border crossing in early May. Mr. Shaibar attributed the smuggling operation to Bedouin families with a footprint in both Gaza and the Egyptian Sinai.

The looting is a product of the anarchy that has gripped much of Gaza as Israel’s war against Hamas enters its 10th month. Israeli forces have targeted Hamas’s governing apparatus and police without installing any new administration in their place, creating widespread lawlessness.

Even as deprivation in southern Gaza has deepened amid a new wave of Israeli military evacuation orders, the contents of over 1,000 aid trucks have been stuck for weeks at the Gazan side of the Kerem Shalom crossing, according to the Israeli authorities. Fearing attack, aid agencies have hesitated to send trucks to collect and distribute the goods.

Israel says it has made efforts to ensure U.N. agencies can collect the goods, including by paving new roads, and points out that private merchants have been able to bear the difficult conditions to pick up their wares. Aid officials say Israel could do much more, including allowing them to expand their use of other roads and crossings.

Convoys ferrying U.N. aid are often an easier target than private businessmen, who are willing to pay hundreds or thousands of dollars in protection money to guards or to the organized gangs themselves.

U.N. and Israeli officials said the smugglers outside Gaza were closely coordinated with organized groups inside the territory that have blocked aid trucks with light arms, clubs and improvised roadblocks. After successfully halting convoys, the looters often appeared to know precisely where to find the cigarettes hidden inside, Mr. De Domenico said.

“These attacks have been very targeted,” he said. “They go exactly into the pallet” where the cigarettes are.

Col. Elad Goren, a senior official in COGAT, the Israeli agency that oversees Palestinian civilian affairs, said the smuggling appeared to originate in Egypt; other people familiar with the trade shared his assessment.

“Most of the packages we’ve been able to get our hands on,” Colonel Goren said. “But we believe that things need to be done on the Egyptian side in order to stop the smuggling.”

The Egyptian government’s press office did not immediately respond to a request for comment.

One cigarette seller in Gaza City said prices could range up to $40 per cigarette for more sought-after brands. Desperate smokers were willing to pay the high prices, despite being impoverished after several months of war, he said.

The seller, who spoke on condition of anonymity because he feared retribution, said Hamas forces were still present in the area but not as police to apply the law, just as “mafias.”

General Fuks also expressed dismay over an increase in settler violence in the West Bank, which is home to about 2.7 million Palestinians and a Jewish settler population that has grown to well over 500,000. An extremist minority of violent settlers, he said, had been undermining Israel’s reputation internationally and sowing fear among Palestinians. “That, to me, is not Judaism,” he said. “At least not what I was raised on in my father’s and mother’s home. That is not the way of the Torah.”

Israel seized control of the West Bank from Jordan in 1967 during a war with three Arab states, and Israeli civilians have since settled there with both the tacit and explicit approval of the government, living under Israeli civil law while their Palestinian neighbors are subject to Israeli military law.

The international community largely views Israeli settlements in the West Bank as illegal, and many of them are illegal under Israeli law but are tolerated by the government. Many outposts that began as illegal under Israeli law have subsequently been legitimized by the government, and Palestinians have long argued that they are a creeping annexation that turns land needed for any independent Palestinian state into an unmanageable patchwork.

Last year, the United Nations reported that attacks on Palestinians in the West Bank had surged in the weeks following the Oct. 7 attacks that set off the war in Gaza between Israel and Hamas, with at least 115 killed, more than 2,000 injured and nearly 1,000 others forcibly displaced from their homes, citing violence and intimidation by Israeli forces and settlers.

General Fuks argued that terrifying the Palestinians living alongside Jews was “a dangerous mistake” and that the actions of violent Jewish settlers threatened Israel’s security.

But Mr. Smotrich has been vocal about wanting Israel to claim all of the West Bank. Last month, he struck a deal with ministers to release some money withheld from the Palestinian Authority in exchange for the legalization of five more Jewish outposts, and last week, the finance ministry released about $136 million.

Mr. Smotrich said in a post on social media that day that he was working with planning authorities on approving more than 5,000 additional housing units in the West Bank. “We’re building the good country and thwarting the creation of a Palestinian state,” he said.

Last month an Israeli ministry approved the largest seizure of West Bank land since the 1993 Oslo Accords between Israel and the Palestinians, claiming about five square miles in the Jordan Valley, according to Peace Now, an Israeli group that monitors settler activity. Israel has seized roughly nine square miles of the territory this year, making 2024 by far the peak year for appropriations, Peace Now said.

While settlers and ministers are defiant, their activities are a source of tension for Israel with other nations, including its ally the United States, at a time when it is increasingly isolated in the world over its conduct of the war in Gaza.

“Settlements continue to be counterproductive to a two-state solution,” John Kirby, the national security spokesman for the White House, said in a briefing with reporters on Monday. “We don’t support that.”

Johnatan Reiss contributed reporting.