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.
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."
Neither the White House nor her family have given the circumstances behind her death.
But White House spokesman Josh Earnest said regardless of the cause, ultimately it was IS who was responsible for her death because they were the ones holding her.
"That means they are responsible for her safety and her well-being. And they are therefore responsible for her death," he said.
Three other US citizens - journalists James Foley and Steven Sotloff, and aid worker Peter Kassig - were beheaded by IS.
Mr Earnest said at least one other US citizen was being held hostage in the Middle East, without elaborating.
The militants' claims that Ms Mueller was killed by a Jordanian air strike were dismissed by Jordan as propaganda.
Washington has also cast doubt on the claims, with Mr Earnest saying there was "no evidence of civilians in the target area prior to the coalition strike taking place".
Ms Mueller worked with a number of humanitarian organisations at home and abroad.
She travelled to the Turkey-Syria border in 2012 to work with refugees.
Prominent foreign IS hostages killed:
- Sergey Gorbunov, a Russian engineer, thought to have been killed April 2014
- James Foley, US journalist, killed August 2014
- Steven Sotloff, US journalist, killed September 2014
- David Haines, British aid worker, killed September 2014
- Alan Henning, British aid worker, killed October 2014
- Abdul-Rahman Kassig, US aid worker, killed November 2014
- Moaz al-Kasasbeh, Jordanian pilot, killed January 2015
- Haruna Yukawa, Japanese military contractor, killed January 2015
- Kenji Goto, Japanese journalist, killed January 2015
- Kayla Jean Mueller, US aid worker, killed February 2015, according to IS in coalition air strike
Foreign hostages released by IS:
- Marc Marginedas, Javier Espinosa and Ricardo García Vilanova, Spanish journalists, released March 2014
- Didier François, Edouard Elias, Nicolas Hénin and Pierre Torres, French journalists, released April 2014
- Federico Motka, Italian aid worker, released May 2014
- Five Doctors Without Borders workers (Swiss, Danish, Belgian, Swedish and Peruvian citizens) released April-May 2014
- Daniel Rye Ottosen, Danish journalist, released June 2014
- 46 Turkish hostages and 3 Iraqis including employees of the Turkish consulate, their families and special forces police, released September 2014
- Toni Neukirch, German citizen, also released