Ms Mueller, pictured in 2007. She travelled to the Turkey-Syria border to work with refugees
The US has confirmed the death of aid worker Kayla Mueller, the last American hostage known to be held by Islamic State (IS) militants in Syria.
Her family said they were "heartbroken" to learn the news, and released a letter written during her captivity.
Paying tribute to her, President Obama said "she represents what is best about America".
Last week, Islamic State said she had died in a Jordanian air strike, without providing proof.
Ms Mueller, 26, was abducted while working in Aleppo, Syria in 2013.
"Our hearts are breaking for our only daughter, but we will continue on in peace, dignity, and love for her," her family said in a statement.
In a letter written in 2014, Ms Mueller tries to reassure her family, saying that she had been treated with "utmost respect + kindness".
"I could only but write the letter a paragraph at a time, just the thought of you all sends me into a fit of tears," she wrote.
"I know you would want me to remain strong. That is exactly what I am doing."
'Legacy endures'
Ms Mueller's death was determined after her family was contacted privately by her IS captors over the weekend, with US intelligence then confirming the details of the message.
The Muellers released new photos of their daughter after her death was confirmed
Ms Mueller studied at Northern Arizona University
The family released this letter written while Ms Mueller was being held, parts of which have been redacted
"She has been taken from us, but her legacy endures, inspiring all those who fight, each in their own way, for what is just and what is decent," President Obama said in a statement.
"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."
Neither the White House nor her family have given the circumstances behind her death.
Ms Mueller was the last known US hostage to be held by IS. Three others - journalists James Foley and Steven Sotloff, and aid worker Peter Kassig - were beheaded by the group.
The militants' claims that Ms Mueller was killed by a Jordanian air strike were dismissed by Jordan as propaganda.
Ms Mueller worked with a number of humanitarian organisations at home and abroad.