"I feel I was robbed," Lewis said on ABC's Good Morning America. "He should be a man and admit it. I felt I won the fight hands down. I felt I was a much more superior boxer than Evander."
Holyfield, sitting alongside the British champion, countered: "The fight was in the judges' hand. Once the fight is in the judges' hand, then it's in the judges' hand.
"If Lennox knocks me out, then it wouldn't be no problem. If I knocked him out, it wouldn't be no problem. The judges wouldn't be necessary. Unfortunately, when you have two good fighters and nobody gets knocked out, then it's a matter of opinion."
The American champion also intends to keep Lewis waiting for another chance. "In six months if he wants to get it on we'll get it on," Holyfield said.
However, politics could still intervene and delay the re-match further. Negotiations will be even more contentious between pay-per-view boxing rivals HBO, which backs Holyfield through the promoter Don King, and Showtime, the network with which Lewis has a long-term deal.
Lewis, who earned half of Holyfield's $20m (pounds 12.5) purse, is sure to want a better deal to fight again. He would also like it be held in Britain, which will not appeal to Holyfield.