“It’s not just about the number of trucks coming in the border,” Mr. Lockyear said in an interview on Saturday. “It’s about what happens after that point. It is about the delivery. It is about sustained health care. It is about clean water.”

In its ruling on Thursday, the I.C.J., the United Nations’ highest court, called on Israel to increase the number of land crossings for aid and demanded that it ensure its military doesn’t violate Palestinians’ rights under the Genocide Convention, “including by preventing, through any action, the delivery of urgently needed humanitarian assistance.”

Israel’s Foreign Ministry responded by saying that Israel had gone to great lengths to mitigate harm to civilians and to facilitate the flow of aid into Gaza, “including in particular food, water, shelter equipment and medicines.”

On Oct. 9 — two days after the Hamas attack into southern Israel and the start of Israel’s war in Gaza — Israel imposed what it called a “complete siege” of the territory. Since then, aid has been allowed into Gaza only under restrictive measures that Israel controls; those rules also apply to aid sent by the United Nations and groups like Doctors Without Borders, which is known by its French acronym, M.S.F.

This past week, Mr. Lockyear said, an M.S.F. truck carrying medical supplies and equipment was prevented from entering Gaza because it was carrying metal devices that are used to help set broken bones. “These items, which were formerly approved to go in, we have got them into Gaza previously,” Mr. Lockyear said. This time, he said, “the whole truck was turned around because these items were there, and we don’t know why.”

A spokeswoman for the Israeli authority responsible for allowing aid into Gaza said the authority could find no record or information about an M.S.F. truck being rejected or refused.

Israel has previously said that it prevents or restricts entry of what it calls “dual-use” items — materials or items that it says Hamas could use for military purposes.

Mr. Lockyear said his five-day visit to Gaza, both in the southern city of Rafah as well as Deir al Balah in the central part of the territory, underscored for him the crucial importance of not only ensuring that sufficient aid gets into Gaza and is properly and safely distributed, but also the need to end the conflict itself.

The compounding effects of the humanitarian disaster and the continued military operations came into focus, he said, during a visit to Al Aqsa Hospital in Deir al Balah on March 19, the morning after the area endured another heavy bombardment.

The wards and corridors were full of wounded victims with burns, shrapnel wounds and crushed limbs, including some in need of amputation. Meanwhile, a steady stream of weak and bony children suffering from malnutrition was being brought in.

“One of the most shocking things there is the decision that the medical teams there were having to make, in terms of: Do they give beds to trauma patients, or do they give beds to malnourished kids?” he said.

On Saturday, the director general of the World Health Organization, Tedros Adhanom Ghebreyesus, called for increased evacuations out of Gaza. With battered hospitals struggling to care for the sick and injured, he wrote in a post on X, “around 9,000 patients urgently need to be evacuated abroad for lifesaving health services, including treatment for cancer, injuries from bombardments, kidneys dialysis and other chronic conditions.”

He urged Israel to approve more evacuations, saying, “Every moment matters.”