“Hang on, we’re coming”: Those were the words of President Biden Tuesday at the White House, raising hope for the release of hostages held by Hamas in Gaza even while Prime Minister Netanyahu urges caution. 

“I’ve been talking with the people involved every single day,” Mr. Biden told a reporter who asked about diplomacy involving a hostage deal. “I believe it’s going to happen, but I don’t want to get into detail.”

The statement led Israeli newscasts, and it was soon after Mr. Netanyahu cautioned that he would rather refrain from commenting until the hostages are freed. “If and when concrete information emerges, we will report it,” he said. “Our hearts are with the abductees and their families. Since the start of the war we have been working ceaselessly to release them.” 

Mr. Biden’s words raised hope among family members of the 240 hostages kidnapped on October 7, including the elderly, women, men, and tots as young as a 10-month-old known in Israel as “Baby Kfir.” Yet, premature public statements could lead to false expectations and harden Hamas’s demands. 

As leaked reports indicate that diplomacy involving America, Israel, Egypt, and Qatar is progressing, Israeli officials are expressing skepticism that Hamas can deliver on promises made by its Qatari benefactors. 

The head of Shabak, Israel’s equivalent of the FBI, Ronen Bar, arrived at Cairo, Egypt, Tuesday, in what was seen as a signal that a deal could be imminent. The foreign minister, Eli Cohen, met Tuesday with the International Committee of the Red Cross president, Mirjana Spoljaric Egger, at Geneva. He demanded she work more diligently to get signs of life and deliver medications to elderly hostages, including a cancer patient. 

A possible outline of a deal involving the release of several dozen hostages, mostly women and children, has been reported  widely. In return, the Israel Defense Force would pause Gaza operations for days, Israel would free convicted Hamas prisoners, and fuel would be delivered to the strip. 

Israel’s Channel 11 television reported Tuesday that a possible first phase could include “children for children” — a swap of kidnapped Israeli babies and youngsters for Hamas-affiliated teenagers convicted on terrorism charges. 

As speculation grows that a deal would entail a pause in the IDF’s military pursuit of Hamas, the government is vowing to press on with war, at least for now. “I instructed the army to continue its progress, today and in future days,” the defense minister, Yoav Gallant, told reporters Tuesday. Speaking of the hostages, he added, “By what moral authority can we stop fighting as long as Hamas is holding our people?” 

On Monday, Hamas released chilling images of one hostage, a young soldier named Noa Marziano. In a video shot shortly after she was kidnapped to Gaza on October 7, Marziano mouthed texts dictated to her, indicating that IDF bombings endanger the hostages. Hamas indicated she was later killed, and on Tuesday the IDF confirmed her death, relying on its own intelligence of the case. 

Israeli family members of the hostages took to the road Tuesday, launching a several-day protest march toward the government offices at Jerusalem from Tel Aviv. They demanded the government do more for their release “now,” and some chanted “all of them” in an apparent demand to avoid a partial deal for only some hostages. 

“We are doing everything we can, operationally, intelligence-wise, and diplomatically,” the IDF spokesman, Rear Admiral Daniel Hagari, said Tuesday. A day earlier he took reporters to Gaza’s Rantisi children’s hospital, showing a basement room where hostages were evidently held. A baby bottle left behind as the terrorists and their hostages exited the place was apparently used for feedings. 

Israeli sources indicated that DNA collected in such terrorist lairs could supply intelligence on the hostages’ location. In 1976, an Israeli commando unit managed to release hostages held in a plane hijacked by Palestinian terrorists to Entebbe, Uganda. The hostages were released and the only casualty was the unit’s commander, Yoni Netanyahu, the current premier’s brother.

Similarly, the IDF managed to get one hostage out early in the ground operation. Every combat unit in Gaza is accompanied by intelligence operatives who specialize in hostage release. Yet, with so many hostages cast in different spots around Gaza, a military release of many of them is widely seen as near impossible.

Nevertheless, Israelis believe that as their military operation inside Gaza progresses, a stressed Hamas will be more likely to be forthcoming on hostage releases. “The pressure we apply to Hamas leads to results,” Mr. Gallant said.

Asked about Mr. Biden’s statement, Mr. Gallant said that when it comes to the negotiations, “it’s better to keep them hidden than to make them public.”