US President Barack Obama has confirmed the death of Kayla Mueller, the US aid worker who had been held hostage by Islamic State militants, saying the United States would "find and bring to justice the terrorists who are responsible".

Mueller's family also said in a statement that they were "heartbroken" to learn of her death and released a copy of a letter she had written in 2014 while in captivity.

The comments by Obama and the family come four days after Islamic State said Mueller, a 26-year-old humanitarian worker, was killed on Friday when Jordanian fighter jets bombed a building where she was being held, although Jordan expressed doubt about the Islamist militant group's account of her death.

Mueller was determined to have died after her Islamic State captors contacted her family privately over the weekend, a White House spokeswoman said.

"Over the weekend, the family received a private message from Kayla's ISIL captors containing additional information," National Security Council spokeswoman Bernadette Meehan said, using an acronym for Islamic State.

"Once this information was authenticated by the intelligence community, they concluded that Kayla was deceased," Meehan said.

Neither Obama nor the family gave details of the circumstances of her death.

Mueller was the last-known American hostage held by Islamic State, which controls wide areas of Syria and Iraq. She was taken hostage while leaving a hospital in the northern Syrian city of Aleppo in August 2013.

"No matter how long it takes, the United States will find and bring to justice the terrorists who are responsible for Kayla's captivity and death," Obama said in a statement released by the White House.

"ISIL is a hateful and abhorrent terrorist group whose actions stand in stark contrast to the spirit of people like Kayla," Obama added.