A portrait of the 26-year-old humanitarian aid worker from Prescott, Arizona, came as her death was confirmed by the US government.
Family members spoke fondly of her free spirit and efforts to ease the suffering of others as a small memorial of flowers and handwritten notes took shape in her hometown near a sign calling on people to "Pray for Kayla."
Mueller was captured in August 2013 in Syria, but her captivity had largely been kept secret in an effort to save her.
Few details are known about Mueller's time in captivity and how she died. The Islamic State group claimed Friday that Mueller was killed in a recent Jordanian airstrike targeting the militants.
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The Pentagon said Tuesday that it doesn't know how she died but is certain it was not during the airstrike.
Family members released a letter an imprisoned Mueller wrote last year in which she said she was staying strong and praying.
During a press conference Tuesday outside Prescott's historic courthouse, family and friends remembered Mueller and said that even in the worst circumstances, she focused on the positive.
They said she taught her guards to do crafts and make peace birds out of paper. And she stood on her head for exercise in her cramped quarters.
Beyond those few details, family members have not said what life was like for Mueller in captivity, including whether she was tortured. Three other Americans journalists James Foley and Steven Sotloff and aid worker Peter Kassig were beheaded by Islamic State militants last year.
Gosar told The Arizona Republic that one effort to free Mueller involved a man who traveled to the Syrian prison camp where Mueller was being held. The man told the captors he was Mueller's husband in a ruse designed to free her, Gosar said, but it didn't work.
In addition, Gosar's office said the name of Aafia Siddiqui, a Pakistani scientist convicted of shooting at two US soldiers in Afghanistan, came up in discussions with Islamic State militants over Mueller.