The Yazidi woman, Mr. Carter said, will be reunited with her family as soon as possible. It was unclear on Saturday what would be done with Umm Sayyaf, who, according to Mr. Carter’s statement, is suspected of playing an important role in the group’s activities and “may have been complicit in what appears to have been the enslavement” of the Yazidi woman.

The Yazidis are a religious minority persecuted by the Islamic State.

American interrogators will question Umm Sayyaf about the organization and its operations, but given that she is an Iraqi citizen, authorities there are also likely to seek custody of her, a senior American official said.

Had Abu Sayyaf been captured alive, the official said, the plan was to interrogate him in Iraq and then send him to the United States for criminal prosecution if authorities believed they could build a strong case against him. David Thomson, an analyst and author of the book “The French Jihadists,” said by email that he had confirmed with sources inside the Islamic State that Abu Sayyaf was a Tunisian emir who had traveled to Iraq as far back as 2003. As a member of the first wave of jihadists who arrived in Iraq more than a decade ago, he and his Tunisian colleagues were called “Al Iraqi,” creating confusion over his nationality.

The operation came just months after three unsuccessful raids by American commandos in Syria and Yemen to free American hostages.

In the first one, in Syria last summer, two dozen Delta Force commandos raided an oil refinery in the northern part of the country as part of the effort to free James Foley, an American journalist, but found after a firefight that there were no hostages to be saved.

Mr. Foley was later beheaded by the Islamic State.

In the second, on Nov. 25, American Special Operations forces entered a cave near Yemen’s border with Saudi Arabia in an effort to free Luke Somers, an American photojournalist. But he was not there; the forces freed eight other hostages and killed seven militants.

A few days later, in December, American forces mounted another attempt to free Mr. Somers, storming a village in southern Yemen, but that raid ended in tragedy with the kidnappers killing Mr. Somers and a South African held with him.