The hostages in Gaza are being moved around, with Hamas shuttling some from one apartment to another to obscure their whereabouts, while others are believed to be in tunnels underground.

All the while, at a “fusion cell” quietly formed in Israel last fall, American and Israeli intelligence and military analysts share imagery from drones and satellites, along with communications intercepts and any other information that comes their way that might offer a hint to the hostages’ locations.

More than one war is being waged in the Gaza Strip.

For the most part, the world sees the airstrikes and the ground invasion, which Israel says are aimed at dismantling Hamas and have reduced much of the territory to rubble, setting off a humanitarian crisis. But the rescue on Saturday of four hostages was a reminder that Israel and Hamas are engaged in another, less visible battle:

The militants are determined to hold on to the hostages they seized during their deadly Oct. 7 attack on Israel, for use as human bargaining chips. The Israelis are determined to bring them home.

For more than eight months, the militants have had the upper hand.

Israeli and American officials say they do not know where many hostages are being held. And even when they do, in many cases, a rescue mission is simply not possible.

To date, Israel has rescued a total of seven hostages, but the stark reality is that since the war began, more hostages have died, either in the fighting or at the hands of Hamas. Israel has recovered far more bodies than living hostages.

For all the rejoicing Saturday’s rescues set off in Israel, Israeli and U.S. officials say the complexity of the operation itself and the violence that accompanied it underscored the challenges of finding and extracting hostages. One rescuer died; Israeli commandos killed many Hamas fighters; and many civilians were killed in the crossfire. Hamas also said that three other hostages were killed by Israeli airstrikes, a claim denied by an Israel Defense Forces spokesman.

And it is not clear how many more opportunities for rescue raids there will be, at least aboveground ones. The hostages that have been saved to date have been rescued only from apartments. Now, current and former Israeli and American officials say, Hamas is likely to change tactics, seeking to move more hostages into tunnels and potentially out of reach of commando forces.

The reality, American and Israeli officials say, is that rescue operations will be the exception. Only through diplomatic means will the majority of remaining hostages be brought home. American officials are pressuring Israel and Hamas to agree to a deal that would return hostages as part of a truce.

“One must remember that the release of the four hostages is ultimately a tactical achievement that does not change the strategic aspect,” said Avi Kalo, a lieutenant colonel in the Israeli reserves who once led a military intelligence department that dealt with prisoners of war and missing people. “Hamas still has dozens of hostages, the vast majority of whom, if not all, will not be released in operations, but can be rescued only as part of a cease-fire deal.”

Though freeing the hostages has been a priority since the war began, some American officials say the level of Israeli focus on that goal has varied. The unintentional killing of three hostages in December, when Israeli troops shot three men who had escaped their captors in Northern Gaza, made clear that Israeli troops have not always been attuned to the hostage hunt. The military learned from that mistake, Israeli officials say.

Israeli officials have said that 251 people were believed to have been captured during the Oct. 7 terrorist attacks. An agreement between Israel and Hamas last November led to the release of 105 of them.

Since then, 43 of the remaining hostages have been officially declared dead; many of them, though not all, are believed to have died in captivity. Privately, Israeli officials have said they think fewer than 60 are still alive. American officials have said there are five dual citizens in Gaza who are still alive, and three bodies of Americans being held by Hamas.

Throughout its history, Israel has gone to great lengths to bring home hostages. The long established principle is to use military force as the first option in trying to rescue an Israeli. If rescue is impossible, Israel will make a deal — sometimes giving up more than a thousand Palestinian prisoners for a single captured Israeli soldier.

Tracking the hostages’ movements, an operation in which Britain also plays a role, is not just about establishing location. Military and intelligence officials are also hunting for patterns, trying to learn how long Hamas holds people in one place before moving them to another. If they can discern a pattern, they can better determine the window of time for a rescue operation to be carried out.

The intelligence gathered is often piecemeal. A hint that a particular hostage is still alive, or a clue about what group might be holding the captive, may not reveal an exact location but can give a hint about what part of Gaza to intensify information collection efforts. Though no one can be sure how good that information is, once the Israelis fix a location with a degree of confidence, and believe a hostage may be there for some time, intense planning begins.

Early in the war, some intelligence officials believed most hostages were being held in tunnels. But it appears that living underground has proved tough for Hamas commanders, and that keeping hostages in the apartments of supporters of the organization has turned out to be easier.

As the war has drawn on, Israeli intelligence on the hostages has improved, aided by captured documents and the interrogation of captured Hamas fighters, as well as American and British assistance.

Israeli and American officials believe some hostages may be moving now more than at the beginning of the war. But given the devastating Israeli barrage on the tiny territory, the areas in which Hamas can hide hostages has shrunk, and the opportunities to detect them have grown, U.S. and Israel officials said.

Beyond that, as movement in Gaza became more difficult, communications between Hamas brigades and their central leadership have broken down, according to U.S. officials. As a result, some hostages have remained longer in hiding places.

While American officials believe Hamas has a hand in the treatment of all the hostages, some are not being held by the group, and are instead in the control of allied militant organizations, including Palestinian Islamic Jihad. Because of that, Hamas leadership has seemed unsure how many hostages were in Gaza, according to American and Israeli officials.

Israeli and American officials are increasingly worried about the health of the hostages, who have been subjected to mental and physical abuse over their long captivity.

“You have hostages who are in a very degraded state, mentally and physically, from almost nine months of captivity, and their rescuers may not be able to even recognize them,” said Gen. Richard D. Clarke, a retired head of the U.S. Special Operations Command.

As hard as Israel is looking for the hostages, Hamas leaders are working to keep them hidden — aware that they offer their best leverage in the cease-fire talks.

But they also serve another role. A small group of hostages are believed to be held near Yahya Sinwar, Hamas’s leader in Gaza. They are human shields, and make it harder for Israel to target him.

The Americans and the Israelis have had trouble fixing the precise location of Mr. Sinwar and those hostages. He has moved around Gaza, including hiding below Rafah for a time, and is now likely back under Khan Younis, Gaza’s second-largest city, American officials say. The tunnel network there is vast, and neither the United States nor Israel has been able to fix his precise location, a U.S. official said.

Hamas leaders have also given standing orders to its fighters holding hostages that if they think Israeli forces are coming, the first thing they should do is shoot the captives, according to Israeli officials. If hostages were killed on Saturday, as Hamas claims, it might have been at the hand of the militants, not because of an Israeli airstrike. But for now, Israeli and American officials can neither confirm nor refute the Hamas claims.

Since the earliest days after the Oct. 7 attack on Israel, the U.S. military has flown surveillance drones over the Gaza Strip to help aid in hostage-rescue efforts, American officials said. At least six MQ-9 Reapers controlled by Special Operations forces have been involved in flying missions to monitor for signs of life, officials said.

A senior Israeli official said that British and American drones have been able to provide information that Israel’s drones do not collect. The American surveillance drones have largely the same sensors on board as British and Israeli drones, American military officials said, but the sheer numbers of American aircraft means that more territory can be surveilled more frequently and for longer periods of time.

The drones cannot map out Hamas’s vast subterranean tunnel network — Israel is using highly classified ground-based sensors to do that — but their infrared radar can detect the heat signatures of fighters or other people going into or out of tunnel entrances on the surface, officials said.

Intelligence sharing between the United States and Israel related to the war in Gaza initially focused on hostage-recovery efforts, but over time the collaboration expanded, three current or former senior U.S. officials said.

“They are part of the largest intelligence effort ever conducted in Israel, and probably ever,” Colonel Kalo said of the Americans and the British.

Adam Goldman contributed reporting from Washington.

world