The leader of the World Food Program said that parts of the Gaza Strip are experiencing a “full-blown famine” that is spreading across the territory after almost seven months of war that have made delivering aid extremely challenging.

“There is famine — full-blown famine in the north, and it’s moving its way south,” Cindy McCain, the program’s director, said in excerpts released late Friday of an interview with “Meet The Press.”

Ms. McCain is the second high-profile American leading a U.S. government or U.N. aid effort who has said that there is famine in northern Gaza, although her remarks do not constitute an official declaration, which is a complex bureaucratic process.

She did not explain why an official famine declaration has not been made. But she said her assessment was “based on what we have seen and what we have experienced on the ground.”

The hunger crisis is most severe in the strip’s northern section, a largely lawless and gang ridden area where the Israeli military exercises little or no control. In recent weeks, after Israel faced mounting global pressure to improve dire conditions there, more aid has flowed into the devastated area.

COGAT, the Israeli defense agency that oversees Palestinian civilian affairs, strongly rejected Ms. McCain’s assertion, saying that Israel had recently stepped up its efforts to “flood the Gaza Strip with food, medical equipment and equipment for tents.” COGAT also listed several projects to improve conditions in Gaza, including opening the Israeli port of Ashdod for humanitarian aid shipments.

Some 100 trucks, mostly carrying food, now reach northern Gaza every day, a large increase in supplies that was helping drive down soaring wartime prices, according to COGAT. The Israeli agency also said April saw a “great surge” in new aid, with more than 6,000 relief trucks entering Gaza, a 28 percent increase from the previous month.

On the diplomatic front, negotiations resumed in Cairo on Saturday aimed at reaching a cease-fire and an agreement to release Israeli hostages and Palestinian prisoners. A delegation of Hamas leaders traveled to the Egyptian capital, the Palestinian armed group said.

Over the past few days, Israel and mediators in the talks — Egypt, Qatar and the United States — have awaited Hamas’s response to the latest cease-fire proposal, with Hamas signaling that it was open to discussing the Israeli-approved offer. On Friday, Secretary of State Antony J. Blinken said U.S. officials were waiting to see if Hamas “can take ‘yes’ for an answer on the cease-fire and the release of hostages.”

“The only thing standing between the people of Gaza and a cease-fire is Hamas,” Mr. Blinken said at the McCain Institute in Arizona. “So we look to see what they will do.”

Husam Badran, a senior Hamas official, said in a text message that the group’s representatives came to Cairo “with great positivity” toward the proposed deal. “If there is no agreement, it will be because of Netanyahu alone,” he said, referring to Benjamin Netanyahu, the Israeli prime minister.

For weeks, Mr. Netanyahu has vowed that Israeli forces will invade Rafah, where many of Hamas’s remaining military forces are believed to be arrayed alongside some of its leaders. The plan has prompted widespread criticism, including from the Biden administration, fueled by concern for the safety of more than a million displaced Gazans sheltering there.

As of Saturday, Israel had not dispatched a delegation to Cairo to engage in indirect negotiations with the Hamas officials, as Israeli officials had done in previous rounds of talks, according to two Israeli officials who, following diplomatic protocol, spoke on the condition of anonymity.

Even if Hamas announced in Cairo that it had accepted the proposed deal, a truce was unlikely to be imminent, one of the Israeli officials said. Hamas’s approval would be followed by intensive negotiations to hash out the finer details of a cease-fire, and such talks are likely to be protracted and difficult, the official added.

Ms. McCain said a cease-fire could help ease conditions in Gaza.

“It is horror,” she said on “Meet the Press.” “It is so hard to look at, and it is so hard to hear, also. I am so hoping we can get a cease-fire and begin to feed these people, especially in the north, in a much faster fashion.”

The first American official to say there was famine in Gaza during the conflict was Samantha Power, the director of the U.S. Agency for International Development, who made her remarks in congressional testimony last month.

Ms. McCain, the widow of Senator John McCain, was appointed by President Biden as the American ambassador to the U.N. Agencies for Food and Agriculture in 2021 and became head of the World Food Program, a U.N. agency, last year.

An official declaration of famine is made by a United Nations agency, the Integrated Food Security Phase Classification, and the government of the country where the famine is taking place. It is unclear what local authority might have the power to do that in Gaza. Declarations, which are based on measured rates of hunger, malnutrition and death over short periods, are rare. But for aid groups, a famine elevates one crisis above competing disasters and helps them raise money to respond.

Gaza has been gripped by what experts have called a severe human-made hunger crisis. Israel’s bombardment and restrictions in the territory have made delivering aid very difficult. The amount of aid entering Gaza has increased recently, but aid groups say it is far from adequate.

For the first three weeks of the war, Israel maintained what it called a “complete siege” of Gaza, with Defense Minister Yoav Gallant saying that “no electricity, no food, no water, no fuel” would be allowed into the territory. The Israeli military also destroyed Gaza’s port, restricted fishing and bombed many of its farms.

Israel eventually loosened the siege but instituted a meticulous inspection process that it says is necessary to ensure that weapons and other supplies do not fall into the hands of Hamas. Aid groups and foreign diplomats have said the inspections create bottlenecks, and have accused Israel of arbitrarily turning away aid, including water filters, solar lights and medical kits that contain scissors, for spurious reasons.

Volker Türk, the U.N. human rights chief, said in a statement last month that Israel’s policies regarding aid in Gaza could amount to a war crime.

Using starvation of civilians as a weapon is a serious violation of international humanitarian law and a war crime under the Rome Statute, the treaty of the International Criminal Court, or I.C.C.

Israeli and foreign officials told The New York Times last week that they were worried that the I.C.C. was preparing to issue arrest warrants against senior Israeli officials — including potentially over accusations that they prevented the delivery of aid to civilians in Gaza. (They also said they believed that the court was considering arrest warrants for Hamas leaders, which could be issued concurrently.)

Israel has previously vehemently denied placing limits on aid, accusing the United Nations of failing to distribute aid adequately and Hamas of looting supplies. U.S. and U.N. officials have said there is no evidence of that, other than one shipment that Hamas seized earlier this week, which is now being recovered.

However the issue is resolved, there is little doubt that conditions are still life threatening for many Gazans, particularly children suffering from illnesses that make them especially vulnerable. As of April 17, at least 28 children younger than 12 had died of malnutrition or related causes in Gaza hospitals, according to the local health authorities, including a dozen babies under a month old. Officials believe that many more deaths outside hospitals have gone unrecorded.

There have been some improvements to aid flows in recent weeks, and on Wednesday Israel reopened the Erez border crossing, allowing some aid to cross directly into northern Gaza.

Fatma Edaama, a 36-year-old resident of Jabaliya, in northern Gaza, said conditions in her neighborhood were still difficult. Many commodities, such as meat, are unavailable or sold at sky-high prices, she said.

But flour, canned goods and other items had started to flow far more freely and their cost had dropped sharply, Ms. Edaama said. “Earlier there was nothing, people would grind up animal feed,” she said. “Now, we have food.”

Still, foreign officials and aid agencies say more is needed.

“This is real and important progress, but more still needs to be done,” Mr. Blinken told reporters this week after visiting an aid warehouse in Jordan.