WASHINGTON (REUTERS) - US President Barack Obama on Tuesday confirmed the death of Kayla Jean Mueller, an American aid worker who had been held hostage by ISIS (Islamic State in Iraq and Syria) 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 ISIS said Mueller, a 26-year-old humanitarian worker from Arizona, was killed 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 ISIS captors privately contacted her family 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."

A family representative, who asked not to be identified by name, said the family received a private message from her captors over the weekend containing "additional information, which the intelligence community authenticated and deemed credible".

Neither Obama nor the family gave details of the circumstances of her death. US officials said that the family received an email and photo from ISIS that confirmed she was dead.

US officials said they had no evidence to support Islamic State claims that she was killed in a Jordanian air strike, adding the details surrounding her death remained unclear.

"It's unclear from the intelligence picture how she died,"said one US official, speaking to Reuters on condition of anonymity.

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.

The group has beheaded three other Americans, two Britons and two Japanese hostages - most of them aid workers or journalists - in recent months.

"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.

Even after ISIS Friday announced her death on Friday, the family had expressed hope that she was still alive.

On Tuesday, her parents and brother issued a statement saying, "Kayla was a compassionate and devoted humanitarian. She dedicated the whole of her young life to helping those in need of freedom, justice and peace."

The family also released a handwritten letter they said she wrote to them in the spring of 2014 while in captivity. In it, she states that she was "in a safe location, completely unharmed + healthy."

"I have been shown in darkness, light + have learned that even in prison, one can be free," the letter states. "I am not breaking down + I will not give in no matter how long it takes," the letter states.

US Defence Secretary Chuck Hagel said in a statement, "The world is united in condemning ISIL's continued murder and imprisonment of innocents."