Yahya Sinwar, the head of Hamas and the architect of the Palestinian militant group’s Oct. 7, 2023, terrorist rampage across southern Israel, was killed in a raid in the Gaza Strip, Israel said Thursday.

The death put an immediate and emphatic end to the bloody career of the Palestinian radical movement’s best-known figure, but it also raised fresh questions about which direction the government of Israeli Prime Minister Benjamin Netanyahu would take after the security triumph.

President Biden, Vice President Kamala Harris and some in Israel said Sinwar’s death could open diplomatic space to cut a long-sought cease-fire and hostage release deal in Gaza, but many of Mr. Netanhayu’s political allies took it as a sign that Israel should double down on its campaign to crush the Iran-backed Hamas once and for all as a military force.

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“It is time to increase the military pressure and step on the neck of the terrorist organization until its complete defeat,” Itamar Ben-Gvir, one of Mr. Netanyahu’s most hawkish ministers, said in a statement.

In a statement Thursday evening, Mr. Netanyahu sounded like a man not ready to pull back after a string of Israeli military successes against Hamas and Lebanon-based Hezbollah in recent weeks.

“The man who committed the most terrible massacre in the history of our people since the Holocaust, the mass murderer who murdered thousands of Israelis and kidnapped hundreds of our citizens, was eliminated today by our heroic troops,” he said. “We have demonstrated today that all those who try to harm us, this is what happens to them.”

He was quick to note that Israel’s military campaign to wipe out Hamas as a fighting force did not end with Sinwar’s death.

“Hamas will no longer rule Gaza. This is the start of the day after Hamas,” the prime minister said.

Pentagon spokesman Maj. Gen. Patrick Ryder told reporters in Washington that the U.S. played no role in the mission that resulted in the terrorist leader’s death.

For more than a year, U.S. special operations forces and intelligence personnel have been working alongside their Israeli counterparts to track down hostages, including Americans. No Americans took part in the firefight late Wednesday where Sinwar’s body was later discovered.

“This was an Israeli operation. U.S. forces were not directly involved,” Gen. Ryder said.

Secretary of State Antony Blinken, who has labored fruitlessly for months on a Gaza cease-fire deal, was reportedly heading back to the region for more consultations.

Sinwar, 61, was widely considered among the most charismatic and aggressive of Hamas leaders, but the militant group has survived the loss of other senior figures.

“Sinwar’s death could provide the Israelis with an ability to ‘declare victory’ in Gaza,” Khaled Elgindy, a senior fellow at the Washington-based Middle East Institute, said in an analysis of the killing, but “it is more likely that Netanyahu will see Sinwar’s death as an opportunity to ‘finish the job’ and press ahead for total victory.” The primary variable in the equation, he said, was “whether the Biden administration is actually prepared to bring meaningful and public pressure on the Netanyahu government.”

Chance encounter

The target of a massive manhunt by Israeli forces for more than a year, the elusive Hamas leader was apparently killed in a random confrontation with Israeli forces in Tel Sultan in the southern part of the Gaza Strip.

Israel military spokesperson Rear Adm. Daniel Hagari said Israeli forces identified three Hamas militants running from building to building in Gaza’s southernmost city, Rafah, The Associated Press reported. The troops attempted to shoot the militants before they ran inside a building. An Israeli patrol in the neighborhood ordered a bombing of the structure, and Sinwar’s battered corpse was subsequently discovered among the wreckage.

Four Israeli officials said the military took the body of a slain militant to a laboratory in Israel to assess whether its DNA matched that of Sinwar. AP quoted an Israeli military statement that said three militants had been killed during the operation.

Israel’s Kan Radio reported that cash, weapons and fake IDs were also found at the house where the militants were holed up.

Mr. Biden was briefed on the operation while on a flight to Germany, the Agence France-Presse news service reported, and U.S. officials said they were monitoring the situation.

Mr. Biden and Ms. Harris welcomed the death of Sinwar and argued it provided an opening to clinch the cease-fire deal long sought by Washington.

“There is now the opportunity for a ‘day after’ in Gaza without Hamas in power, and for a political settlement that provides a better future for Israelis and Palestinians alike,” Mr. Biden said in his statement. “Yahya Sinwar was an insurmountable obstacle to achieving all of those goals. That obstacle no longer exists.”

Relatives of the estimated 100 Israeli and foreign hostages still believed held by Hamas in Gaza stepped up their pressure campaign on the government to strike a deal that would free their loved ones.

“Netanyahu, don’t bury the hostages,” Elinav Zangauker, whose son is being held by the militants, said in a plea on social media. “Go now to the negotiators and the Israeli public and present a new Israeli initiative.”

Hamas, which is closely allied with Iran, did not issue a statement regarding the Israeli claims. Instead, it posted a warning against false reports and said only messages released by the group on its Telegram account should be regarded as accurate. The statement was silent on the status of Sinwar, The Times of Israel reported.

The AP reported that photos circulating online showed the body of a man resembling Sinwar with a gaping head wound, dressed in a military-style vest, half buried in the rubble of a destroyed building. The photos were taken by Israeli security officials at the scene, according to the wire service account.

The terrorist leader’s death on the battlefield was just the latest success for Israel in hunting down those behind the Oct. 7 massacre. Ismail Haniyeh, long the political leader of Hamas, was killed by a bomb while in Tehran this summer for the inauguration of the Iranian president. Israeli airstrikes and covert operations also have taken out a broad swath of senior Hezbollah leaders, including longtime chief Hassan Nasrullah.

Several top Hamas military commanders have been killed in the fighting that erupted after the Oct. 7 attacks, but Sinwar had long been considered the top target for Israeli forces. He had not been seen in public since a video surfaced three days after the 2023 attack, but he was elevated to the top post in Hamas after Haniyeh was assassinated.

Reports in January said Israeli troops narrowly missed capturing him near his hometown of Khan Younis.

Mr. Biden’s critics in Washington, who have criticized his pressure campaign on Israel to strike a deal, backed Mr. Netanyahu’s call for an escalated campaign against a weakened Hamas.

“The region cannot move forward without the elimination of Hamas as a military entity,” Sen. James E. Risch of Idaho, the top Republican on the Senate Foreign Relations Committee, said in a statement. “… The U.S. and our allies should do more to help the Israelis continue to cut off the head of the snake, and certainly stop trying to get in their way.”

• Mike Glenn contributed to this article, which is based in part on wire service reports.