The 28-year-old tested positive for synthetic testosterone, which he claims entered his body as a result of treatment that he was given to counter abnormally low testosterone levels.
He is adamant that he was unaware that what he was doing was contrary to anti-doping rules and he claims that, until ruled otherwise, his WBA and IBF light-welterweight titles remain rightfully his.
"Let the commission decide, let the sanctioning bodies decide," Peterson told BBC Sport. "Until that point I'm still the champ.
"If the procedure I [had] done is what gave me the dirty urine, then what else can I say? I made a mistake. That's all I can say. Apologise for it and try and move on with my career."
Khan had branded Peterson "a cheat".