The photographs taken by US jailers humiliating prisoners who were naked or hooded, on leashes or piled in a pyramid, rocked the world, becoming one of the few things Bush has said he regretted about the war.
Taguba said that he described to Rumsfeld what he termed the "torture" of "a naked detainee lying on the wet floor, handcuffed, with an interrogator shoving things up his rectum," the magazine reported.
The ex-general, who retired in January, spoke of other, undisclosed material on the Abu Ghraib abuse, including descriptions of the sexual humiliation of a father with his son, who were both detainees.
He also told the magazine he saw "a video of a male American soldier in uniform sodomizing a female detainee," adding that the video was never made public or mentioned in any court or in public.
Taguba said that all high-level officials had avoided scrutiny while the jail keepers at Abu Ghraib were tried in courts-martial.
And how could this have gone unreported?
"From what I knew, troops just don't take it upon themselves to initiate what they did without any form of knowledge of the higher-ups," Taguba told the New Yorker, adding that his orders were to investigate the military police only and not their superiors.