But her family and U.S. government officials say they went to great lengths to try to rescue the 26-year-old humanitarian worker, efforts that ultimately failed. Her parents announced Tuesday they'd received confirmation she had died.
Now they're working to bring her body back from Syria.
U.S. troops may have come close to rescuing Mueller
in July when they staged a daring raid at an abandoned oil refinery near Raqqa in Syria in an attempt to find journalist James Foley, who was executed by ISIS in August, and other hostages.
Several dozen elite U.S. commandos
from units such as Delta Force and Navy SEAL Team 6 flew in aboard helicopters, a U.S. official told CNN, and engaged in a firefight with militants.
Troops found evidence the hostages had been there recently, including writings on the cell walls and hair believed to be Mueller's, one U.S. official said.
"We devoted enormous resources, always devote enormous resources to freeing captives or hostages anywhere in the world," President Barack Obama said
Tuesday in an interview with BuzzFeed News.
Worked with the White House
A spokeswoman for the family said Mueller's parents often communicated with the White House
in trying to free their daughter, who was taken hostage in August 2013.
Last summer, the Muellers asked the Obama administration to consider trading Dr. Aafia Sadiqqi, known as "Lady al Qaeda," in exchange for Mueller, the spokeswoman said. The Daily Beast first reported
on the family's request to the White House.
ISIS has repeatedly called for the release of Sadiqqi, who is serving an 86-year sentence in Texas.
Authorities said she shot at two FBI special agents,
a U.S. Army warrant officer, an Army captain and military interpreters while she was being held unsecured at an Afghan facility on July 18, 2008.
The White House did respond to the family, but the family spokeswoman gave no details on what the answer to their request was.
McCain, Gosar staff tried to help
Other rescue efforts included a trip by Sen. John McCain of Arizona, who went to Iraq and Qatar and met with Syrian rebel leaders to try to secure Mueller's release.
Rep. Paul Gosar, R-Arizona, said one of his aides went to a refugee camp near Kobani, Syria, to look for her.
Gosar said government sources told him a man showed up at a terrorist training camp in Syria claiming to be Mueller's husband. He appealed for her release and wanted to talk to her but was turned away.
The family representative said the man was actually Mueller's boyfriend, who was kidnapped at the same time as Mueller. He'd been released from captivity and went back to try to get Mueller released, the spokeswoman says. He continues to stay in touch with the family.
In clearing up another question, the spokeswoman said that contrary to many media reports, the family never turned down a military rescue mission because it was too risky.
Instead, the family had reached out to the White House and asked for notification if there would be another rescue attempt after the failed mission last July.
Mueller's family has not spoken out against the U.S. government's efforts, but James Foley's brother has complained the government didn't do enough.
"I don't have all the answers, but I do think that a more cooperative approach (is needed)," Michael Foley said. "And there wasn't sharing of information. You wouldn't believe how difficult it was to get information (on) released journalists ... from the ways that we have these walls built."
On Thursday, an official with the Joint Chiefs of Staff said a report in The Daily Beast that alleged the administration failed to act quickly
on British intelligence about the location of the hostages is "clearly false" and "very ill-informed."
The official said once plans were developed and Pentagon had confidence in the ability to carry out the mission, officials made their recommendation to the White House and "quickly" received clearance to carry out the operation.
There was no sitting on intelligence or any delay in acting upon it, the official said.
Bernadette Meehan, National Security Council spokeswoman, said, "U.S. forces conducted this operation as soon as the President and his national security team were confident the mission could be carried out successfully and consistent with our policies for undertaking such operations."