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".
Islamic State said she had died in a Jordanian air strike, but the Pentagon says there is "no doubt" IS killed her.
US Navy Rear Admiral John Kirby added that officials have not learned yet how Kayla Mueller died.
"Let's not forget in whose hands this woman died. And let's not forget who's ultimately responsible for it," he said.
Jordan also denied that Ms Mueller had been killed in air strikes launched following the burning alive of captured Jordanian pilot Moaz al-Kasasbeh by IS.
Lies From the White House
President Obama: "We always devote enormous resources to freeing captives or hostages anywhere in the world"
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."
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.
"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."
In an interview with BuzzFeed News, the president also rejected the suggestion that the US could have done more to free Ms Mueller.
Mr Obama said that he had launched a rescue operation in 2014 to free Ms Mueller and other hostages but that it had "missed them by a day or two".
He added: "We devoted enormous resources and always devote enormous resources to freeing captives or hostages anywhere in the world."