Karr's father, Wexford, and half brother, Nate, told ABC's "Good Morning America" that it was impossible for Karr to have committed the crime.
"Absolutely not. Emphatically, absolutely without a doubt impossible," Nate Karr said.
"I can say almost without question that from the time that John had children he has never missed a Christmas with his family -- and that's any Christmas," he said.
When asked about John Karr's televised statement that he was with JonBenet at the time of her death, Wexford Karr said: "I don't believe a word of it."
Nate Karr rejected accusations that his half brother was obsessed with children.
"He may care overly for children as some people do, but he would never do anything to hurt a child, or molest a child or anything like that. There's been no evidence in the past that he's ever done anything like that, you know, so to me that's just wild speculation."
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