As President Biden seeks a way to end the Gaza war during his final months in power, Israelis are yearning for a pact that would release the hostages being held in Gaza. Will Prime Minister Netanyahu’s first White House visit during his current stint as Israel’s leader yield a deal?

The press on this side of the ocean widely describes the goal of American-led negotiations as “a cease-fire deal”; Israeli counterparts are calling it a “hostage release deal.” Either way, White House officials say a deal is near.

“The gaps are closeable, there is no question about that,” the National Security Council spokesman, John Kirby, said Thursday. Yet, “some compromises have to be made,” he added, and urged Israel and Hamas to make them. 

Arriving at the White House, Mr. Netanyahu thanked the president for decades of support for Israel and warmly said he speaks to him as “a proud Jewish Zionist to a proud Irish American Zionist.”

Hours after his sit-down with the president, and a joint session with families of American hostages, Mr. Netanyahu met the presumptive Democratic presidential nominee, Vice President Harris. Unlike Mr. Biden, she studiously declines to identify herself as a Zionist, a term that Democratic progressives shun. 

Following phone calls with Democratic donors who urged Ms. Harris to display more support for Israel, her husband, Doug Emhoff, who is Jewish, told supporters that the vice president is on the same page as Mr. Biden. She is fully supportive of Israel’s existence as a Jewish state and of its right to defend itself, he reportedly said.

Yet, Ms. Harris made more forceful statements on the need to end the Gaza war and the suffering of Palestinian civilians. A deal proposed quietly by Mr. Netanyahu was made public by Mr. Biden was later written into a United Nations Security Council resolution. Some unresolved details of that deal were at the heart of Mr. Netanyahu’s White House talks Thursday. 

An Israeli team headed by the Mossad chief, David Barnea, will arrive next week at Doha, where it had been scheduled to land Thursday. White House officials and the premier said he wants to first consult with the president before sending the team. Before their White House meeting, however, some hostage relatives reportedly claimed that Mr. Netanyahu is slowing down the negotiations for political reasons. 

Yet, after their meeting with Messrs. Netanayhu and Biden, ‏Hagit and Rubi Chen, whose Israeli-American son, Itay, is held by Hamas in Gaza, reportedly expressed hope that “something will happen in the coming days,” around the hostage deal. 

Washington sources tell the Sun that Mr. Netanyahu indeed has a political reason to temporarily slow down progress on a deal: He is concerned that once he signs one, his far-right partners could dissolve his ruling coalition. As the Knesset next week is scheduled to go on a summer recess, he might be able to ignore his right flank. Either way, the White House, ever so gently, is pushing Mr. Netanyahu to end the war. 

“I’m going to keep working to end the war in Gaza, to bring home all the hostages and to bring peace and security to the Middle East, and end this war,” Mr. Biden said Wednesday during an Oval Office address to the nation. Mr. Netanyahu, in contrast, insists on “complete victory” in Gaza, which would include the end to Hamas and return of all hostages. 

Mr. Netanyahu’s plan reportedly calls for Israeli troops to remain in control of the border area between Egypt and Gaza, known as the Philadelphi Corridor, even as Hamas releases more than two-dozen hostages in the deal’s first phase. Israel would also monitor movement to the northern part of the strip from the south. 

With such conditions in place, Hamas is unlikely to make a deal, Israeli officials told Kan television news. Further, Israelis doubt statements from Hezbollah and Houthi officials that they would end their multi-prong attack on Israel once the war in Gaza ends.

In his Wednesday speech, Mr. Netanyahu made clear that Iran is behind these attacks. One of his top asks in the White House meeting was to hasten America’s arming of Israel, so it can better confront the Iranian threats. Arms are Mr. Biden’s leverage in the twilight of his presidency. 

Also unsaid, but a possible pressure point on Mr. Netanyahu: Even if the premier has to make painful compromises, they would be more favorable for Israel under a president who calls himself Zionist than under a potential future one who shies away from the term.