Rumsfeld says he offered to resign twice

"I felt that he ought to make the decision as to whether or not I stayed on," Rumsfeld said Thursday on CNN's "Larry King Live" program. "He made that decision and said he did want me to stay on."

Rumsfeld indicated that he felt a measure of responsibility for the scandal. At a Senate hearing in May, Rumsfeld said the abuses occurred on his watch and "I take full responsibility."

"The problem is, this kind of thing occurs in prisons across the country and across the world," he said. "And you have to know it's going to be a possibility. And therefore the training and the discipline and the doctrine has to be such that you anticipate that risk. And clearly, that wasn't done to the extent it should."