Two people briefed on the family’s communication with the Islamic State said that her parents had received at least three photos. Two showed Ms. Mueller, who was 26, in a black hijab, or Muslim head covering, that partly obscured her face. Another showed her in a white burial shroud, which is used in traditional Muslim funerals. The images showed bruises on the face, but both people, who reviewed the photographs and asked not to be identified given the sensitivity of the matter, said it remained unclear whether her injuries were consistent with being killed in the rubble of a flattened building, as the Islamic State reported.
The group, also known as ISIS or ISIL, said on Twitter last week that Ms. Mueller had died in a building that had been demolished by Jordanian airstrikes, a claim that both the White House and Jordan’s government said was unfounded.
Yet the images sent to her family did not completely rule out death in that manner.
One of the two people briefed on the evidence said that Ms. Mueller’s face did not show puffiness or other concussive effects associated with a bomb blast, making it unlikely that she was killed when the area was hit, as the Islamic State said. But the same person said that she could have been in a nearby building or struck by flying debris.
Described by friends and family members as a deeply idealistic young woman eager to help those less fortunate, Ms. Mueller was just shy of her 25th birthday on Aug. 4, 2013, when she disappeared in the northern Syrian city of Aleppo.
She had arrived in Syria a day earlier with a Syrian man who has been described as her boyfriend or colleague.
He had been contracted to fix the Internet connection at a Doctors Without Borders office, and employees of the international charity were flabbergasted when Ms. Mueller showed up with him.
Syria was then a no-go zone for most international aid workers, said employees of the charity, who explained that they had reluctantly housed her overnight and agreed to drive her to a bus station for what was supposed to be her trip back to Turkey.
Her car was ambushed on the way, and she and her Syrian companion were abducted. He was later freed and has declined to speak about what happened.
Once in the hands of the militants, Ms. Mueller was forced to wear the hijab and was placed in a cell with female detainees, according to two former hostages held in the same facility.
