Transcript for Part 3: They Left Our Daughter 'To Be Tortured and Raped'
Everyone, if you are receiving this, it means I am still detained. Reporter: The voice isn't Kayla's, but the words are, coming from the secret Isis prison where she was held in the Syrian desert. Please know that I am in a safe location, completely unharmed and healthy, put on weight in fact. Reporter: After eight months of silence, Kayla's words now appeared in a letter in her handwriting, smuggled out by the women from doctors without borders, who had been released. Know I am also fighting from my side in the ways I am able, and have a lot of fight left inside of me. Not only was she alive, she was strong still. Do not fear for me and continue to pray. All my everything, Kayla. Reporter: But with no way to contact the kidnappers, the muellers could only wait for the next step, unaware that officials at doctors without borders at their headquarters in Brussels had purposely withheld for almost two months that very contact information brought out by Kayla's fellow hostages. The women were given this e-mail to negotiate for Kayla and didn't even give it to us, much less do anything to help her or help us. We could not share it with you because of our safety concerns for our staff. Reporter: The group's director for Syria said she had waited for all of her staff to be free, in a phone conversation recorded by the tearful muellers. Would your staff negotiate for Kayla? No, because it will be difficult for us to negotiate for Kayla. The crisis management team that we have installed for our five people will be closed down in the next week. Because our case is closed. They left her there. They deserted her. They were instructed by the hostage takers, "Negotiate for this woman." Reporter: And they did not. They did nothing and wouldn't help us. It just seems hopeless, you know? You'll send that e-mail right away after we hang up? We prefer to send it tomorrow if that's okay? Well, not really. We'd like to get it to our contact as soon as possible. Every day to us is a critical time. Every hour. Okay. Yes. Okay. Yes. At least we got an e-mail. Reporter: Few humanitarian groups in the world are more highly praised than doctors without borders, known overseas as msf, the letters of its name in French, medecins Sans frontiers. Msf operates in places where there are wars, natural disasters. They're a fabulous organization, and they do wonderful work. But somewhere in a boardroom, they decided to leave our daughter there to be tortured and raped. Reporter: Kayla was in a doctors without borders vehicle when she was captured by Isis in Syria, but the organization said nonstaff members are not its responsibility. We could not take steps to negotiate for her freedom. Reporter: Why not? Because we can't be in the business of negotiating for people who don't work for us. And to do so would also have increased the risk that our teams already face. Reporter: The executive director of doctors without borders usa, Jason cone, says the group never would have allowed an American to come to its hospital in Syria if it had known of Kayla's plans in advance. Reporter: But once she was taken, wasn't she your responsibility? No, she wasn't our responsibility anymore. Reporter: Was there no moral responsibility? I don't think there was a moral responsibility. I don't understand how a humanitarian organization can justify doing that. Reporter: Finally, in late may, 2014, it was Isis which made contact with the muellers in this e-mail, likely written by one of the british Isis guards. This message is to inform you that we have the American citizen, Kayla Jean Mueller, prisoner. We don't want to harm her. She's like a guest with us at the moment. They're telling you they're open to negotiation. Reporter: Chris Voss, who once ran the FBI's international hostage negotiation team, says the e-mail and the earlier video were clear signs that a deal could get done with Isis. This is, "We have something that you want. We want you to believe you can get her out because we want something for her." Reporter: Even though she's an American and America says it doesn't negotiate? Right. Because they know that if -- if given the opportunity, families will find a way. The conditions of Kayla's returning home safely are no media involvement whatsoever, and a cash payment. Kayla's a commodity unfortunately. They make an opening offer. They want some sort of counteroffer to continue the conversation. Reporter: Another good sign -- Isis would allow Kayla to answer three personal questions to prove she was alive. Carl wrote back -- How did you get stitches in your eyebrow as a child? Her older brother Eric was pulling her in a wagon and it tipped over. Reporter: Correct. What did you teach your niece to say, music is -- Music is everywhere. Reporter: Correct. What is your friend Moe's real name? Her name is Monica. Reporter: All correct. It was Kayla. Mom and dad, I'm still remaining healthy. You should have already received the three answers to the proof of life questions you provided. Reporter: Even better than the e-mails, a followup with Kayla's actual voice, laying out the kidnappers' latest demands, including the release of a Pakistani woman being held in a U.S. Prison. Those detaining me are demanding an exchange of Dr. Aafia Siddiqui's release for my release. If this is not achievable, they are demanding five million euros to ensure my release. Good-bye. They're saying she can still be released. Reporter: Working with Kayla's former campus minister, reverend Kathleen day, the muellers began what would be a remarkable exchange of some 27 e-mails between the Arizona couple in their kitchen and the terrorists holding their daughter in Syria. They were focused every day, every waking moment, every sleeping moment, on what they could do to get Kayla back. Reporter: The muellers' answers were all crafted by FBI agents assigned to the case from the very beginning. And reverend day began to be worried by what other aid groups had told her about working with the U.S. Government in hostage situations. What was the concern? That if you worked with the state department that you'd never get your people out. Reporter: And soon the muellers began to have their own doubts. You asked to meet with president Obama? He refused. We did meet in the white house with many high-ranking officials but he did not see us. Reporter: And no one in the white house told them what was about to happen. U.s. Special forces, which have carried out a number of successful high-risk rescue missions, like this one, had been authorized to launch a secret rescue operation for Kayla and some 18 other hostages. It turned out that the hostages were no longer at that location. Reporter: It was a dry hole. They just missed them. I deployed an entire operation at significant risk to rescue not only her, but the other individuals that had been held, and probably missed them by a day or tw Reporter: One week later, in Arizona. We got a nasty e-mail from Isis that said because of what your arrogant government attempted to do, your daughter has 30 days to live. If you fail to meet this deadline we will send you a picture of Kayla's dead body. It was Kayla's birthday that was the deadline for them to kill her. This will be our first act of revenge taken for the miserably failed and unsuccessful attempt by your arrogant government to free their prisoners.
This transcript has been automatically generated and may not be 100% accurate.