The United States has warned Israel that it must fight more surgically and avoid further mass displacement of Palestinians in its war against Hamas to avoid a humanitarian crisis that overwhelms the world’s ability to respond, according to senior Biden administration officials.

The White House has told Israel that replicating the scale of its bombardment in northern Gaza as it makes an expected push into southern Gaza once the recent pause in fighting ends would produce a crisis beyond the capacity of any humanitarian support network, the officials said on Monday night. The United Nations has said the fighting has already displaced most of Gaza’s population of 2.2 million.

The statements are the Biden administration’s strongest warning to Israeli officials to date about the next phase of their military operation. For weeks, the White House has been careful to say it does not dictate how Israel conducts its military operations, but President Biden and senior members of his staff have grown more vocal as the humanitarian crisis has unfolded.

They also come as the administration officials, who spoke on the condition of anonymity to discuss sensitive diplomatic issues, said they were ramping up humanitarian aid during the cease-fire that took effect last week, and expressed optimism that aid could continue even when fighting resumed.

Among other things, American officials have told the Israelis that any coming military operations should not hamper the flow of power and water or impede the work of humanitarian sites such as hospitals and U.N.-supported shelters in south and central Gaza.

The Israeli government was receptive to the requests, one official said.

The cease-fire, to allow for the exchange of hostages held by Hamas and Palestinians taken prisoner by Israel, has allowed for the first extended break in the violence since the Oct. 7 attack by Hamas gunmen and other militant groups killed an estimated 1,200 people in Israel. Gazan health officials say at least 13,000 people were killed during the nearly 50-day Israeli bombardment and ground invasion that followed.

Israel’s prime minister, Benjamin Netanyahu, has made clear that he intends for Israel to continue fighting after the truce ends, though it was extended by two more days on Monday.

The Biden administration officials said the United States was planning to take advantage of the extra time. On Tuesday, the United States will begin deploying military relief flights to deliver medical items, food, winter items and other necessities for the civilian population to Egypt, which borders Gaza.

Extraordinary progress has already been made in aid delivery, the officials said, though they acknowledged that the level of assistance was not enough to support normal life in Gaza. The officials also said that the increase in aid, including much-needed fuel, was not contingent on hostage releases, offering hope that the shipments could continue when fighting resumed.

John F. Kirby, a spokesman for the National Security Council, said on Monday that since the pause in fighting had taken effect, Gaza had received its largest humanitarian convoy since the war began. The convoy brought the total number of aid trucks to over 2,000 since Oct. 21, he said.

Mr. Kirby said that the administration would “take advantage of every hour of every day that there’s a pause to try to help the people of Gaza.”

“Our team has prioritized getting this much-needed relief into Gaza to alleviate the suffering of Palestinian civilians there,” Mr. Kirby said. “Of course, most of them have nothing to do with Hamas.”