He added, “It is all about building an understanding of the organization and how it functions.”

The two prisoners seized by Delta Force commandos were in American custody, Gen. Mark A. Milley, the chairman of the Joint Chiefs of Staff, told reporters on Monday, but he declined to give details.

General Milley described roughly how the commandos had discovered Mr. al-Baghdadi hiding in the tunnels. In the Iraqi broadcast interview, Mr. Sajid, Mr. al-Baghdadi’s brother-in-law, described how the Islamic State leader had lived in underground tunnels, equipped with a library of religious books, a ventilation system and lights. He described one of the tunnels Mr. al-Baghdadi had lived in as a bunker that was about eight yards long and about five yards wide.

In the interview with Mr. Sajid, which was broadcast by Al Arabiya Hadath, he said that when Mr. al-Baghdadi changed locations he had traveled in two white Toyota pickups accompanied by five men.

A senior State Department official said on Monday that American forces also had killed Abu Hassan al-Muhajir, the man believed to be the deputy of Mr. al-Baghdadi, over the weekend. Mr. al-Muhajir also served as a spokesman for the terrorist group, the official said. The operation took place in the area of Jarabulus near the Euphrates River, the official added, and a militia led by Syrian Kurds played a big role.

Also on Monday, General Milley spoke by telephone to his Russian counterpart, Gen. Valery Gerasimov, the chief of the Russian General Staff. The two had spoken about Syria earlier in October, as part of the efforts to de-conflict American and Russian operations in Syria. General Milley also spoke to Gen. Nicholas Carter, the United Kingdom’s Chief of Defense Staff.

Intelligence officials are expected to scour the new material for information about ties between Mr. al-Baghdadi and the Islamic State’s affiliates in other countries. That could help the American government better understand how quickly the affiliates could move in a different direction from the core Islamic State group without Mr. al-Baghdadi.

“It will also provide useful insights into the extent to which Baghdadi exerted operational control over ISIS remnants in other countries,” said Norm Roule, a former C.I.A. officer and expert on the Middle East.