Isis fighters claimed Mueller, who was seized in the Syrian city of Aleppo in August 2013, was killed in a February 6 coalition air strike that buried her in rubble.
US officials have pushed back, saying the circumstances of the 26-year-old aid worker's death remain unclear.
Kayla Jean Mueller died while being held by Isis. Photo / AP
The girl's father expressed strong reservations about the longstanding US policy of refusing to negotiate with or pay ransom to foreign groups that have kidnapped Americans, as the Mueller family broke its media silence.
"We understand the policy about not paying ransom," Carl Mueller told NBC television's "Meet the Press."
Other Western countries, in contrast, are known to have paid large ransoms to free hostages.
The interview with Mueller, his wife Marsha and his son Eric was conducted Saturday. Excerpts aired Sunday, with the full interview set for broadcast tomorrow on other NBC programs.
Asked whether President Barack Obama's administration did enough to free her daughter, Marsha Mueller said: " I think they wanted to. But I think again, it's the policy. And I don't think anyone had any idea this group would be as powerful as they were."