A risky predawn raid by U.S. Special Operations forces that resulted in the death of the Islamic State’s leader on Thursday was set in motion months ago with a tip that the top terrorist was hiding out on the top floor of a house in northwest Syria.

In brief remarks at the White House, President Biden said the decision to send about two dozen helicopter-borne commandos to capture or kill the leader, Abu Ibrahim al-Hashimi al-Qurayshi, was made to minimize the risk of civilian harm. Military officials said attacking with bomb or a missile would have been safer for the troops but could have endangered more than a dozen civilians in the house, including several children.

“We made a choice to pursue a Special Forces raid, at a much greater risk than our — to our own people, rather than targeting him with an airstrike,” Mr. Biden said. “We made this choice to minimize civilian casualties.”

Aides said Mr. Biden had approved the raid on Tuesday morning after months of military planning, including dozens of rehearsals and an exercise involving a tabletop model of the building. On Thursday, he called the operation a warning to all terrorist groups. “This operation is testament to America’s reach and capability to take out terrorist threats no matter where they try to hide anywhere in the world,” he said.

In the end, Mr. Biden said, Mr. al-Qurayshi died when he exploded a bomb that killed him as well as members of his own family. Rescue workers said women and children were among at least 13 people killed during the assault.

Pentagon officials said that 10 civilians, including eight children, had been safely evacuated, and that commanders would review whether the mission had caused civilian harm.

The two-hour raid came days after the end of the largest U.S. combat involvement with the Islamic State since the end of the jihadists’ so-called caliphate three years ago. American forces backed a Kurdish-led militia in northeastern Syria as it fought for more than a week to oust Islamic State fighters from a prison they had occupied in the city of Hasaka.

The battle for the prison killed hundreds of people and offered a stark reminder that even after the collapse of the caliphate, the group’s ability to sow chaotic violence persists, counterterrorism specialists said.

The American assault, carried out by about two dozen Army Delta Force commandos backed by Apache helicopter gunships, armed Reaper drones and attack jets, resembled the raid in October 2019 in which Abu Bakr al-Baghdadi, the previous leader of the Islamic State, died when he detonated a suicide vest as U.S. forces raided a hide-out not far from where Thursday’s operation took place.

Defense Secretary Lloyd J. Austin III, tacitly acknowledging a recent spate of reports of U.S. airstrikes killing civilians, said the Pentagon would review whether the raid had caused any civilian casualties. Last week, Mr. Austin ordered the military to strengthen its efforts to prevent civilian deaths and to improve the way it investigates and acknowledges claims of civilian harm in U.S. combat operations.

For Mr. Biden, the success of the operation was a welcome relief from the looming threat of a Russian invasion of Ukraine. It was important for another reason: After the Taliban takeover of Afghanistan last year, there was widespread concern that the U.S. evacuation would give ISIS a new opportunity to retake territory. The director of the C.I.A., William J. Burns, told Congress that efforts to collect intelligence about local ISIS operations could suffer.

Speaking in the Roosevelt Room at the White House, Mr. Biden was understated as he described the history of the ISIS leader, saying that he had ordered a series of atrocities, including against the Yazidi people.

Little is known about the ISIS leader, whose real name is Amir Muhammad Said Abdel-Rahman al-Mawla, or other members of the group’s senior command. But his death was a significant blow to the terrorist group, analysts said.

While he was nowhere near as prominent as his predecessor, “Mr. Qurayshi still commands a lot of respect within jihadi circles and is known to be highly intelligent and able to think strategically,” said Colin P. Clarke, a counterterrorism analyst at the Soufan Group, a security consulting firm based in New York.

Indeed, after Mr. al-Qurayshi replaced Mr. al-Baghdadi, the United States put a bounty of up to $10 million on his head.

Mr. Clarke said that Mr. al-Qurayshi, who was 45 and born in Iraq, had kept a low profile, which helped him elude an American-led manhunt but also may have hampered his ability to expand the Islamic State’s global network and brand. In March 2019, ISIS lost the last piece of its territory, which once stretched across parts of Syria and Iraq.

According to two senior administration officials who spoke on condition of anonymity to discuss the operation, an unspecified intelligence tip had placed Mr. al-Qurayshi in the Atmeh area of Idlib Province and then, by early December, more specifically at a stand-alone, three-story cinder block building surrounded by olive trees.

Images shared on social media by activists who visited the site showed simple rooms with mats on the floors, a diesel heater and clothes and blankets scattered about, some of them covered with blood.

American officials said Mr. al-Qurayshi and his family lived on the third floor. He left the building only occasionally to bathe on the rooftop. He relied on a top lieutenant who lived on the building’s second floor and who, along with a network of couriers, carried out his orders to ISIS branches in Iraq and Syria, and elsewhere in the world without using electronic devices whose signals Western spies could intercept — a practice Osama bin Laden used for years.

Top Pentagon officials and military commanders apprised Mr. Biden of their planning, at one point presenting a model of the building where the ISIS leaders and their families lived — and noting that a Syrian family with no apparent connection to the terrorist group was living on the first floor.

Mindful of the danger to civilians and to the commandos, military engineers told Mr. Biden that they did not believe the entire building would collapse if Mr. al-Qurayshi detonated a suicide vest or larger explosives on the third floor. They proved correct.

Opting for a ground raid allowed the commandos to try to safely evacuate civilians from the building — something not possible in an airstrike, which might flatten the building. In the end, no Americans were hurt.

Shortly after the commandos arrived, warnings shouted in Arabic over bullhorns urged occupants on the first floor — as well as anyone else — to evacuate. One man, one woman and four children fled the first floor.

Not long after that, Mr. al-Qurayshi detonated his explosives — much bigger than a suicide vest — in a blast so powerful that bodies, including his own, were blown out the window.

“He killed himself and his immediate family without fighting, even as we attempted to call for his surrender and offered him a path to survive,” Gen. Kenneth F. McKenzie Jr., the head of the Central Command, who oversaw the mission, said in a virtual security conference sponsored by the Middle East Institute on Thursday.

Following the blast, commandos stormed the building and engaged in a firefight with Mr. al-Qurayshi’s top lieutenant and his wife, who were barricaded on the second floor with their children. Both were killed, as was one child, but four children were safely evacuated.

American officials said most of the casualties resulted from the explosion on the third floor and fighting on the second floor.

In complex raids, the military’s initial version of events may be incomplete. Accounts of past operations have at times turned out to be contradictory or wrong, and Mr. Kirby warned that the Pentagon was still collecting information from the assault.

Mr. Biden, along with Vice President Harris, Mr. Austin and Gen. Mark A. Milley, the chairman of the Joint Chiefs of Staff, monitored the mission late Wednesday from the White House Situation Room.

At one particularly tense moment in the operation, a U.S. helicopter ferrying commandos to the building experienced a mechanical problem — a drivetrain failure, Mr. Kirby said. It flew to a location well away from the target site, where commanders determined it could not be readily repaired, and was destroyed by rigged explosives and U.S. attack aircraft.

At another moment at the end of the operation, several armed men linked to Al Qaeda approached the house in a menacing manner. In a brief firefight, two militants were killed and several others fled, officials said.

Mr. Kirby said that military forensics experts identified Mr. al-Qurayshi using fingerprint and DNA analysis, and left his remains at the site. Mr. Kirby said the American troops took no prisoners or civilians into custody. But he indicated that the commandos collected materials such as cellphones and computer hard drives — as is customary in this kind of operation — that analysts will pore over for clues on combating ISIS.

Asked about the timing of the raid, Mr. Kirby said multiple factors played a role: intelligence levels, certainty about the ISIS leader’s location, weather and operational conditions (it was a virtually moonless night, ideal for night operations).

“A lot of factors had to line up to be just right,” said Mr. Kirby. “This was the best window to execute the mission.”

Mr. Kirby said the fight against ISIS and other extremist groups will continue. “They’re still a threat,” he said. “No one’s taking a victory lap.”

Ben Hubbard reported from Beirut. David E. Sanger, Helene Cooper, Julian Barnes and John Ismay contributed reporting from Washington.