The Israeli unit that supervises aid deliveries into Gaza, COGAT, said on Monday that 322 trucks carrying humanitarian supplies were inspected and transferred to the territory on Sunday and that more than 70 percent of them carried food. That figure was the highest since the start of the war, it said.

But UNRWA, the primary United Nations agency aiding Palestinians, said that 103 aid trucks crossed into Gaza on Sunday.

The two sources often disagree on the volume of aid reaching the enclave, but the latest discrepancy was especially striking, and the reasons for it were unclear.

Until now, almost all aid for Gaza has entered through two southern border crossings, at Rafah and Kerem Shalom. Israel has recently allowed limited use of a third crossing farther north. Aid groups accuse Israel of restricting deliveries, which Israel denies; COGAT said Sunday on social media, “There is no limit to the amount of aid that can be facilitated for the civilians in Gaza,” repeating a line it has used for month.

Israel said last week that it would use the Erez border crossing into northern Gaza and the Israeli port of Ashdod, around 20 miles northeast of Gaza, to allow supplies to reach the territory. The threat of famine is most acute in the north.

The United States hopes that 350 aid trucks will enter Gaza each day by later this week, the State Department spokesman, Matthew Miller, said on Monday, adding that the Biden administration expects Israel to ensure “a sustained” increase in aid deliveries to the territory.

Speaking at a daily news briefing, Mr. Miller said that Israel had taken “initial positive steps over the past few days” after President Biden warned Prime Minister Benjamin Netanyahu that U.S. policy toward Israel could change if more is not done to feed and protect the people of Gaza.

Aid workers caution that any solution to the hunger crisis, which the United Nations says borders on famine, requires a sustained increase in the amount of aid that enters the territory as well as more medical staff trained in how to treat the effects of malnutrition. They also say it is unwise to look at a single day’s figures, given daily fluctuations, and that, above all, a cease-fire is needed so that civilians and humanitarian staff can operate in safety.

Before the conflict, around 500 commercial and aid trucks entered Gaza each day. Since Oct. 7, when Israel announced a siege of the territory, the number of trucks has varied but on average around 106 have entered Gaza each day, according to the U.N. data. For its part, COGAT’s figures show an average of around 115 trucks entering per day.

Juliette Touma, a spokeswoman for UNRWA, said that Gaza needs 500 trucks of aid each day, for weeks and months, to remedy the crisis.

In the short term, the situation in north Gaza could worsen. The seven aid workers killed last week worked for World Central Kitchen and had been working to deliver hundreds of tons of aid that had arrived by ship to northern Gaza. The organization has since suspended its operations in Gaza, and the World Food Program said it only managed to get 47 trucks of aid to north Gaza, something it called a “drop in the ocean of need.”

The United States Central Command said it had airdropped aid to northern Gaza by parachute on Sunday. Several governments have conducted airdrops over Gaza in recent weeks but aid officials say that they are less efficient than overland deliveries.

Michael Crowley contributed reporting.