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 Feb. 10 by her family and U.S. 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 26-year-old international aid worker, who grew up in Prescott, Arizona, was captured in August 2013 after leaving a Doctors Without Borders hospital in Aleppo, Syria.
Mueller's brother and parents spoke to "Today" host Savannah Guthrie. The family has declined repeated requests for an interview with The Associated Press.
Mueller'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."
"I actually asked the president that question when we were in the White House," he said without elaborating.
Mueller's parents said in the interview that the U.S. government put policy ahead of American lives.
White House spokesman Josh Earnest said Monday that the Mueller family had been put in a difficult position by the U.S. policy against making concessions to terrorists, but he defended it as being in the best interests of the nation.
"The president is confident that his administration did do everything that was possible within the confines of that policy - using our military might, using our intelligence capability, using our diplomatic influence - to try to secure the safe release and return of Kayla Mueller," Earnest said.
A recent Associated Press-GfK poll found that only 3 in 10 Americans think the United States should pay a ransom to save an American hostage overseas, even if it's the only way to rescue the hostage. A quarter of Americans say there are circumstances when the United States should directly negotiate with a terrorist group.
The poll of 1,045 adults was conducted online Jan. 29-Feb. 2. The margin of sampling error for all respondents is plus or minus 3.5 percentage points.
The Obama administration has defended the Bergdahl swap. Some U.S. lawmakers were outraged by the exchange of five Taliban commanders held at the Guantanamo Bay prison for the Idaho native who left his post in Afghanistan and was captured and held by the Taliban for five years.
The Joint Chiefs of Staff unanimously supported the exchange, insisting that the United States has a sacred commitment to men and women who serve that it never will leave anyone behind on the battlefield.
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