“There were two women — both wives, both wearing vests,” Mr. Trump said at the White House, in response to a question about whether one of Mr. al-Baghdadi’s wives had tried to detonate an explosive vest as commandos closed in. “They never detonated. But they were dead.”

On Wednesday, a senior State Department official said he could not confirm Turkish reports that Mr. al-Baghdadi’s wife, sister and other members of his family had been captured. He also said the State Department knew “almost nothing” about Mr. al-Baghdadi’s successor, Abu Ibrahim al-Hashemi al-Qurayshi.

The official, who briefed journalists on the condition that he not be named, said that Mr. al-Qurayshi “appears to be a nobody” and that based on what little that is known about him, “we’re not impressed.”

“If he is in Iraq or Syria, we don’t think he is too long for this world anyway,” the official said. He would not say whether Mr. al-Qurayshi had ever been detained by American forces, as Mr. al-Baghdadi was early in the Iraq war.

Turkish officials have been keen to emphasize Turkey’s role in fighting terrorism and pursuing Islamic State members since Mr. al-Baghdadi’s death in a house a few miles from the Turkish border in an area where the Turkish armed forces operate.

Officials published photographs of three people they identified as Mr. Baghdadi’s elder sister, Rasmiya Awad, 65, her husband and a daughter-in-law, and said they had been detained by Turkish security forces several days ago. The three were living along with five children in a trailer near the town of Azaz, officials said.

“Much dark propaganda against Turkey has been circulating to raise doubts about our resolve against Daesh,” Fahrettin Altun, the Turkish presidency’s director of communications, said on Twitter, using another name for the Islamic State. “We have been leading in the fight against terrorism in all its forms.”