A group of relatives of American hostages who met with Mr. Netanyahu on Monday said that if his speech does not announce a deal to return the roughly 120 hostages still in Gaza — around 40 of whom are believed to be dead — it would be “an absolute failure.”

But if Mr. Netanyahu signals that he might agree to the current deal, he could alienate the far-right members of his fragile coalition government.

“We are here in Washington to make clear to the world that the Israeli people want a deal — and if Netanyahu refuses to reach one, he must resign,” said Zahiro Shahar Mor, a nephew of Abraham Munder, who remains captive in Gaza after more than nine months. Other members of the Munder family were released as part of a temporary cease-fire deal late last year.

But some far-right ministers in Mr. Netanyahu’s ruling coalition have threatened to abandon the bloc if he closes the deal with Hamas. They want the group eradicated through military force instead. Mr. Netanyahu has sent mixed messages about the deal’s prospects, giving rise to criticism at home and abroad that he could be stalling.

“This visit prioritizes his personal political survivability over our shared interests,” a group of more than 30 Israeli luminaries from the defense, industry, academia, law and public service sectors told the bipartisan group of congressional leaders who invited Mr. Netanyahu to speak, in a letter dated Tuesday and shared with reporters.

Mr. Netanyahu’s visit has brought thousands of activists from around the country to protest his conduct of the war in Gaza. The war has killed more than 39,000 Palestinians, according to Gazan health authorities; displaced nearly everyone in Gaza; and caused widespread destruction, disease and hunger.

While protesters marched in Tel Aviv, calling for a hostage deal, about 400 American Jews, including two dozen rabbis, rallied in a House office building on Tuesday, ahead of Mr. Netanyahu’s speech, leading to arrests by the Capitol Police.

Mr. Netayanhu will meet with President Biden on Thursday in Washington. He is also set to meet with Kamala Harris, the vice president and Democratic presidential contender, who has been more critical of Israel’s conduct of the war.

On Friday, the prime minister will travel to Florida to visit Donald J. Trump, the former president and Republican presidential nominee, with whom he has had a close, though sometimes strained, relationship. Mr. Trump has supported the expansionist policies of Mr. Netanyahu’s far-right government and retains the support of his most extreme coalition members.

“Amoon was the first to be diagnosed two months ago,” she said last week, adding that the 10-year-old girl developed a stomachache, stopped eating, started vomiting and looked pale. “I couldn’t see how yellowish she was because it is very dark inside the store.” Her other two children, Kenzy 15, and Kandi, 11, followed soon after.

More than 100,000 people in Gaza have contracted acute jaundice syndrome, or suspected hepatitis A, since the war between Hamas and Israel began on Oct. 7, the World Health Organization said last week.

It is just one disease that has spread rapidly in Gaza as most of the territory’s 2.2 million people have fled their homes, forced to live in squalid, crowded camps and makeshift shelters, while basic needs like clean water, sewage treatment, trash collection, soap and fuel for cooking have grown scarce.

There are also nearly one million cases of acute respiratory infections, half a million cases of diarrhea and 100,000 cases of lice and scabies, the W.H.O. said. On Friday, the agency’s chief, Dr. Tedros Adhanom Ghebreyesus, said that even polio, a disease that has been eradicated in much of the world, was present in Gaza. A variant of poliovirus has turned up there in six samples of water or wastewater, he said, meaning that some people there are infected, though no symptomatic cases have been reported.

Dr. Hanan Balkhy, the W.H.O. director for the eastern Mediterranean region, told members of the news media: “In the Gaza Strip, where garbage and sewage fill the streets, cases of acute respiratory infections, diarrheal illnesses, acute jaundice syndrome and skin infections are surging. The situation is indeed dire.”

People with hepatitis A usually recover fully within weeks or a few months, but some become seriously ill and a small number die. (It is unrelated to the more serious and long-lasting hepatitis B and C, which spread through blood contact.)

In the developed world, diarrheal illnesses and diseases like hepatitis A are relatively rare, and often not very serious. But in chaotic and crowded places with poor sanitation and malnutrition, they become much more common and dangerous. Since the war began, aid workers have warned of the threat of more serious epidemics in Gaza like cholera, which can quickly lead to mass mortality, but so far those have not materialized.

The disease spread in Gaza has coincided with Israeli airstrikes and ground combat in and around hospitals and clinics, damaging nearly all of them and forcing many to close. The large number of people treated for war injuries — almost 90,000, Gaza’s health ministry says — and the surge in illness have overwhelmed Gaza’s diminished medical system.

Dr. Balkhy said that more than 1,000 attacks on health care have been reported since Oct. 7. Israel’s military says that Hamas has stationed fighters and military equipment in hospitals as well as beneath them to take advantage of the cover they provide, a charge that Hamas and hospital officials dispute.

The Israeli military has launched two operations at Gaza’s largest hospital, Al-Shifa, fighting deadly battles with militants there. An investigation by The New York Times found evidence that Hamas had stored weapons in tunnels beneath the hospital but could not confirm the Israeli claim that it was a Hamas command and control center.

Before the war, Gaza’s health care system was “reasonably well functional,” said Dr. Rik Peeperkorn, the W.H.O.’s representative to Gaza and the West Bank. Now, fewer than half of its facilities remain even partly operational, he said, and its health care work force is severely depleted.

Israel has promoted the establishment of new field hospitals to expand medical infrastructure for civilians in Gaza, according to COGAT, the arm of the Israeli military that implements policy in the occupied West Bank and Gaza.

On Sunday, the Israeli military shot at a convoy run by UNRWA, the main U.N. agency for Palestinians, the U.N. said. The UNICEF vehicles that came under fire on Tuesday were near the same area as the earlier attack, but the U.N. said it was still not clear who was responsible.2

The Israeli military did not immediately respond to a request for comment.

The war in Gaza has been the deadliest conflict for the United Nations in the history of the organization, with 198 staff members killed and its facilities attacked hundreds of times, Stéphane Dujarric, a U.N. spokesman, said. Many workers from other humanitarian organizations have also been killed. The United Nations said last month that Gaza had become the most dangerous place in the world for aid workers.

“There is international law that protects them,” Mr. Dujarric said, “but the way for the law to protect them is for people to actually respect the law, respect the rules, respect the work of humanitarian workers.”

Photographs posted on social media by Adele Khord, UNICEF’s regional director for the Middle East and North Africa, showed bullet holes in one of the vehicles in Tuesday’s convoy. Ms. Khord said it was the second UNICEF convoy to be fired on in Gaza over the past four months, adding that “the humanitarian consequences could have been severe, for both our teams and the children they serve.”

Despite the attack, UNICEF workers in two cars were able to complete the mission, continuing on to Gaza City to pick up the five children, Kurtis Cooper, a spokesman for UNICEF, said. “The children were successfully reunified with their father,” he said.

The head of UNRWA, Philippe Lazzarini, said the attack on his agency’s convoy had involved “heavy shooting” that forced his team to duck and take cover. One of the cars was so heavily damaged it had to leave the convoy.

Louise Wateridge, a member of UNRWA’s communication team with the convoy, said bullets had ripped through the car in which she was riding in the front passenger seat. They missed her.

“Our safety should not be down to luck,” Ms. Wateridge wrote in a post on X on Tuesday.

Matthew Mpoke Bigg contributed reporting from Jerusalem.