U.S. aid worker Kayla Mueller, held hostage by Islamic State militants for 18 months, is dead, her family said on Tuesday, but the circumstances were unclear and President Barack Obama vowed to hunt down the culprits.

Mueller's family received an email and photograph over the weekend from her captors that enabled American intelligence to determine that she had been killed, U.S. officials said.

Islamic State said on Friday that Mueller, 26, was killed when Jordanian fighter jets bombed a building where she was being held outside Raqqa, a stronghold in Syria of the Islamist militant group. Jordan and U.S. officials have expressed doubt about Islamic State's account of her death.