The American, who took Khan's WBA super-lightweight and IBF light-welterweight belts in a controversial split points decision in Washington last December, told a televised news conference on Tuesday that he was training already.
Peterson said he accepted the rematch because the fans wanted it, and not because of pressure from Khan's people or any feeling that he had to prove himself.
"It seems like Team Khan still have problems over what happened in DC, I can only tell them that nothing shady happened in DC but I'm pretty sure they won't take my word on it," added the 27-year-old.
Khan's camp criticised referee Joseph Cooper in the first fight for docking their man two points for pushing and also questioned the presence of a 'mystery man' in a hat seen on television talking to a ringside judge.
The man was later identified as Mustafa Ameen, an IBF volunteer helping cash-strapped boxers, who denied interfering with scorecards. The WBA ordered a rematch, however.
"I want to tell Team Khan you all have your chance to make things right. I'm looking forward to a good fight. I'll be training just as hard as you," said Peterson, who goes into the fight with a 30-1-1 record.
"You say your training camp started two weeks before you normally do. Well, I've been training since that day we stepped out of the ring. So I'll be prepared and ready, ready to die in that ring to keep these titles."
David Itskowitch, chief operations officer for Golden Boy Promotions, said the fight was being billed as "No Doubt" because both men wanted to leave no doubt about who was the champion.
Khan said he had a lot of respect for Peterson but still felt he had won the first bout.
"It hurts me watching it," said the 2004 Olympic lightweight silver medallist. "The next fight there won't be any mistakes.
"I have tasted defeat before and you all saw how I've come back from that. You'll see me come back from this defeat a lot stronger, a lot better and a lot more focused."