The Muellers supported Trump's 2016 presidential campaign.
Mueller's family learned their daughter was killed in February 2015, but the circumstances surrounding her death have remained unclear.
"He either killed her or he was complicit in her murder", Carl Mueller said. "The chairman of the joint chiefs of staff named the operation that took down al-Baghdadi after Kayla Mueller, after what she had suffered", he said.
In the emotional interview Mr Mueller said the evil ISIS leader had raped his daughter several times during her time in captivity. "It makes a big difference when you are talking to these people with a humanitarian attitude". It's horrific to look at them, she looks lifeless to me, but then we started getting these messages saying she wasn't gone and don't be surprised if ISIS did this.
"One of the Beatles [their name for ISIS guards] started to say, 'Oh, this is Kayla, and she has been held all by herself".
"At that time, ISIS was being more truthful to us than the last administration", Marsha said.
In 2015, the Obama administration was criticized for a US -led mission that targeted four prisoners at a prison in ISIS-held territory. The requests were denied, and they're considering taking legal action to receive documents related to her death.
"We are so grateful for them", she said, according to The Arizona Republic.
Over the weekend, Carl said that the operation to kill al-Baghdadi in northern Syria-confirmed on Sunday by President Trump-was named after Kayla.
It is believed that she was killed in 2015 during coalition airstrikes, however her cause of death has not yet been confirmed by the US government.
United States special operations commandos struck the hideout overnight Saturday, swooping in on helicopters and chasing the IS founder into a tunnel where he detonated a suicide vest, according to the U.S. account of the raid.
Aside from Mueller, ISIS terrorists were also behind the deaths of freelance journalists James Foley and Steven Sotloff, as well as Peter Kassig, a humanitarian worker, killed in 2014.
"Think of the things he did to Kayla". This raid was impeccable and could only have taken place with the acknowledgment and help of certain other nations and people. "And then the next day, Nancy Pelosi comes out and says she was upset that he told Russian Federation and he didn't tell the House Intelligence Committee".
He kept her in his captivity, his personal captivity. He was an animal.
Trump called the ISIS terrorist a "gutless animal" as he announced his death.
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