"The strain of not knowing where their daughter is at and whether or not she is alive or not is something that is starting to wear on them," Geiler said. "But if we had to go on ahead and say in a word how they're doing, they're hopeful for her safe return."
The parents are asking the nation and the world to pray for Mueller's return, he said. "This thing, it's time to have an ending. It's time to bring Kayla home to her parents and her family," Geiler said.
The Islamic State group said Friday that Mueller died in a Jordanian airstrike. The government of Jordan dismissed the statement as propaganda. U.S. officials said they have not seen any evidence to corroborate the report.
Mueller is the only known remaining U.S. hostage held by the Islamic State group. She was taken hostage in August 2013 while leaving a hospital in Syria.
Her parents and a few close friends kept Mueller's situation a closely guarded secret to ensure her safety. Since her identity was publicized Friday, they have stayed out of public view but released a short statement addressed to Islamic State.
"You told us that you treated Kayla as your guest, as your guest her safety and well-being remains your responsibility," Mueller's family said.
Meanwhile, the road leading to their Prescott home remains blocked off by Yavapai County Sheriff's Office vehicles. In downtown Prescott, Mueller is on the minds of most people. Tourists stop to look at a handmade "Pray for Kayla" sign at the corner of a busy street.
Mueller is an aid worker who previously volunteered with organizations in India, Israel and the Palestinian territories. She had been working in Turkey assisting Syrian refugees, according to a 2013 article in The Daily Courier, her hometown newspaper.
"She knew where she was headed," Geiler said. "She knew what she wanted to do. There was compassion and caring for those less fortunate. She always wanted to help somebody in need."
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