“If we can scoop somebody up alive, with their cellphones and diaries, it really can help speed up the demise of a terrorist group like ISIS,” said Dell L. Dailey, a retired commander of the military’s Joint Special Operations Command and the chairman of the Combating Terrorism Center at West Point.

American military and intelligence officials caution that the Islamic State is far from defeated, particularly with a sophisticated propaganda apparatus that continues to inspire and, in some cases, enable its global following to carry out attacks. But in the self-proclaimed caliphate across swaths of Iraq and Syria, the terrorist group’s last two major strongholds are under siege, many senior leaders have fled south to the Euphrates River Valley, and its legions of foreign fighters are battling to the death or slipping away, possibly to wreak havoc in Europe.

The race to drive the jihadists out of eastern Syria, where they have held sway for three years, has gained new urgency as rival forces converge on ungoverned parts of the region. Syrian forces and Iranian-backed militias that support them are advancing east, closer to American-backed fighters battling to reclaim Raqqa. Russia threatened on Monday to target American and allied aircraft the day after the United States military brought down a Syrian warplane.

This highly volatile environment puts an increasing premium on the Special Operations missions.

Despite his nom de guerre, Mr. Uzbeki, 39, was a native of Tajikistan, not Uzbekistan, and honed his fighting skills with the Islamic Movement of Uzbekistan, a Taliban-allied jihadist group, according to an American military official. About 10 years ago, he moved to Pakistan, where he had extensive contacts with Al Qaeda, the official said. In recent years, he had moved to Syria and joined the Islamic State’s fighting ranks.

Mr. Uzbeki was close to Mr. Baghdadi, the Islamic State’s leader, and helped plot a deadly attack on a nightclub in Istanbul on New Year’s Day. He was targeted for his role in the Islamic State’s plotting of attacks around the world, said Col. John J. Thomas, a spokesman for the United States Central Command. “He facilitated the movement of ISIS foreign terror fighters and funds,” Colonel Thomas told reporters in April.