The militants increased their demands after the May swap for Army Sgt. Bowe Bergdahl, Eric Mueller told NBC's "Today" in an interview that aired Monday.
"That made the whole situation worse because that's when the demands got greater," he said. "They got larger. They realized that they had something."
Mueller's death was confirmed February 10 by her family and US officials. The Islamic State group claimed she died in a Jordanian airstrike, but U.S. Officials have not confirmed that. The Pentagon said it didn't know how she was killed.
The young woman's father, Carl Mueller, said that the United States' willingness to swap for Bergdahl but not pay ransom or allow ransom to be paid for his daughter "was pretty hard to take."
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"I actually asked the president that question when we were in the White House," Carl Mueller told NBC without elaborating.
Some US lawmakers were outraged by the exchange of five Taliban commanders held at the Guantanamo Bay prison for Bergdahl, an Idaho native who left his post in Afghanistan and was captured and held by the Taliban for five years.