(Reuters) -- President Barack Obama and the family of U.S. aid worker Kayla Mueller confirmed on Tuesday that the last-known American hostage held by Islamic State militants had died, with Obama promising to "find and bring to justice the terrorists who are responsible."
U.S. officials said the family received an email and photograph over the weekend from her captors that confirmed her death but said the circumstances in which she died remained unclear.
Mueller, 26, was captured in August 2013 while leaving a hospital in the northern Syrian city of Aleppo. She previously had been working in Turkey providing humanitarian assistance to refugees from Syria's bloody civil war.
Islamic State said on Friday that Mueller was killed when Jordanian fighter jets bombed a building where she was being held outside Raqqa, a stronghold of the Islamist militant group.
Jordan and U.S. officials have expressed doubt about the account of her death offered by Islamic State, an al Qaeda offshoot that controls wide areas of Syria and Iraq.
Mueller's family said in a statement on Tuesday that they were "heartbroken" to learn of her death and released a copy of a letter she had written in 2014 while in captivity.
"Over the weekend, the family received a private message from Kayla's ISIL captors containing additional information," White House 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.
Mueller was Islamic State's only American woman hostage known to have died. 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, who last year ordered American air strikes targeting Islamic State positions, 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.
Obama offered his condolences to Mueller's parents Marsha and Carl, and her brother Eric, saying "Kayla represents what is best about America."
"Kayla's compassion and dedication to assisting those in need shows us that even amongst unconscionable evil, the essential decency of humanity can live on," Obama said.
U.S. 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. Two U.S. government sources said that it appears most likely that she was killed in some kind of combat situation in which her captors were unable to keep her safe.
"It's unclear from the intelligence picture how she died," said one U.S. official, speaking to Reuters on condition of anonymity.
Even after Islamic State Friday announced her death on Friday, the family had expressed hope that she was still alive.
"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," they wrote in their statement on Tuesday.
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" and had been treated with "the utmost respect + kindness."
"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.
Mueller, a 2009 Northern Arizona University graduate, had worked for a Turkish aid organization on the Syrian border and previously volunteered for schools and aid organizations abroad including in the West Bank, Israel and India.
Her family's statement quoted from a letter they said she sent to her father on his birthday in 2011.
"I will always seek God. Some people find God in church. Some people find God in nature. Some people find God in love; I find God in suffering. I've known for some time what my life's work is, using my hands as tools to relieve suffering," the 2011 letter stated.
U.S. Secretary of State John Kerry said that "ISIL, and ISIL alone, is the reason Kayla is gone."
"Like our friends in Jordan, our resolve is unshaken to defeat this vile and unspeakably ugly insult to the civilized world and to defeat terrorists whose actions - killing women, killing children, burning people alive - are an insult to the religion they falsely claim to represent," Kerry said.
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