Kayla Mueller wrote her family a heart-wrenching letter nearly a year ago, possibly from the bowels of a Raqqa, Syria, building that U.S. special forces raided on July 4, 2014, only to learn Mueller - and at least three other hostages who were later killed - had been moved days earlier.

"If you could say I have 'suffered' at all throughout this whole experience it is only in knowing how much suffering I have put you all through," wrote Mueller, a 26-year-old aid worker from Arizona who was kidnapped in Syria by ISIS in August 2013.

"I have a lot of fight left inside of me. I am not breaking down + I will not give in no matter how long it takes," Mueller said in the newly released letter, believed to have been written in the Spring of 2014. "I know you would want me to remain strong. That is exactly what I am doing. Do not fear for me, continue to pray as will I + by God's will we will be together soon."

Click here to read Kayla Mueller's letter to her family

Mueller's parents confirmed Tuesday their daughter died while in the hands of the terror group, though they did not say how or when she was killed. A source familiar with the communications told Fox News that the terror group sent Mueller's parents a photo, taken from the neck up, of their daughter to prove she was dead.

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"We are heartbroken to share that we've received confirmation that Kayla Jean Mueller has lost her life," Carl and Marsha Mueller, of Prescott, Ariz., said in a statement. "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 received information from their daughter's ISIS captors over the weekend that was authenticated, according to U.S. officials.

"On this day, we take comfort in the fact that the future belongs not to those who destroy, but rather to the irrepressible force of human goodness that Kayla Mueller shall forever represent."

- President Obama

"The family received a private message from Kayla’s ISIL captors containing additional information," National Security Council spokeswoman Bernadette Meehan said Tuesday. "Once this information was authenticated by the intelligence community, they concluded that Kayla was deceased."

ISIS claimed last week she was killed by a Jordanian airstrike, but offered no immediate evidence. White House Press Secretary Josh Earnest said Tuesday the family was unable to determine Mueller's "precise cause of death" or the timing of it. Earnest noted there was no evidence of civilians in the area prior to Jordan's strike on a weapons compound in Raqqa, Syria, he said had been hit before. 

"What is not possible to call into question is that ISIL, regardless of her cause of death, is responsible for it," Earnest said.

The Pentagon, meanwhile, said it is certain Mueller did not die in one of the Jordanian airstrikes. When asked Tuesday if there was any doubt who killed Mueller, Navy Rear Adm. John Kirby replied, "No doubt. ISIL."

President Obama said in a statement earlier that Mueller, a 2009 graduate of Northern Arizona University, "represents what is best about America, and expressed her deep pride in the freedoms that we Americans enjoy, and that so many others strive for around the world."

"In how she lived her life, she epitomized all that is good in our world," he said of Mueller. "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. "

"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," he said. "On this day, we take comfort in the fact that the future belongs not to those who destroy, but rather to the irrepressible force of human goodness that Kayla Mueller shall forever represent."

Images of children suffering in the early stages of Syria's ongoing civil war prompted Mueller to leave her home in Prescott, Ariz., in December 2012, to work with the Danish Refugee Council and the humanitarian organization Support to Life to help refugees. According to a family spokesperson, Kayla found the work heartbreaking but compelling.

Mueller was captured on Aug. 4, 2013, in Aleppo, Syria -- 10 days before her 25th birthday -- while leaving a Spanish hospital staffed by the international humanitarian group Doctors without Borders.

According to an intelligence source, Mueller was kidnapped along with her Syrian boyfriend, who was let go days later. He went back to convince ISIS to free Mueller but was unsuccessful, the source told Fox News.

Jordan has been launching airstrikes against the extremist group in response to a video released this week that shows captive Jordanian pilot Lt. Muath al-Kaseasbeh being burned to death in a cage.

Al-Kaseasbeh, whose F-16 came down in December while conducting airstrikes as part of a campaign against the militants by a U.S.-led coalition, was believed to have been killed in early January.

Mueller is one of four Americans to die while being held by Islamic State militants. Three other Americans -- journalists James Foley and Steven Sotloff, and aid worker Peter Kassig -- were beheaded by the group.

Earnest said Tuesday that at least one other American is being held captive in the region. Though Earnest did not name the hostage or the captor, it is believed Austin Tice -- a U.S. marine turned journalist -- is being held by al-Nusra, Al Qaeda's Syrian affiliate.

At approximately 3 a.m. on July 4, 2014, U.S. special operations troops launched a hostage rescue attempt in Syria at a jihadist base known by terrorists as the "Usama bin Laden Camp." The troops failed to find the hostages and were forced to withdraw after a gun battle with ISIS militants, according to the Pentagon.

U.S. intelligence sources told Fox News the White House knew of the hostages' exact location eight months ago -- at the end of May 2014 -- but did not sign off on the raid until six weeks later. The reason for the delay is not known.

ISIS set up a Twitter account in October 2014 to communicate with the family of American Peter Kassig, a military veteran and aid worker whom they later executed. To show their credibility, an ISIS tweet told the Kassig family to send the terror group's regards to "Carl and Marsha Mueller."

Obama spoke to Mueller's parents, offered his prayers and condolences and, "committed that we will relentlessly pursue the terrorists responsible for Kayla’s captivity and death," Meehan said. 

In confirming her death Tuesday, the Mueller family quoted another letter the young woman penned to her father on his birthday in 2011.

"I find God in the suffering eyes reflected in mine. If this is how you are revealed to me, this is how I will forever seek you," Kayla wrote in the letter.

"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," she wrote.

Friends and family gathered Tuesday afternoon to publicly share stories about a young woman who was driven by a calling to help those who are suffering. 

"What was so extraordinary about Kayla was that she did ordinary things to extraordinary measures," said friend Kathleen Day, head of United Christian Ministry at Northern Arizona University where Mueller attended. "She gave people food. She gave people water."

Mueller's closest childhood friend, Eryn Street, described her as having "great empathy" for others.

"It's hard to find that in this world -- it's really rare," she told reporters. "It was her greatest strength."

Mueller's maternal aunt, Lori Lyon, also spoke, saying her niece was "always standing up for people who were suffering and wanting to be their voice."

"She has done more in her incredible 26 years than many people can ever imagine doing in their lifetime," Lyon said. "Kayla has touched the heart of the world."

Fox News' Catherine Herridge, Jennifer Griffin and Cristina Corbin contributed to this report.