"Sicko," Moore's latest movie, focuses on the healthcare industry.
ABC's "This Week with George Stephanopoulos" arranged the debate, Variety reported Friday, but Moore pulled out, saying he had agreed to debate former Rep. Billy Tauzin, R-La., who left Congress to become the pharmaceutical industry's top lobbyist.
"Instead of informing the viewers that Mr. Tauzin would not debate me and allowing me on the air, (ABC) proposed a debate with Tom Delay, a man who currently has nothing to do with the specific issues raised in the film 'Sicko' and is under indictment," Moore said in a statement.
DeLay said Moore would not provide a copy of "Sicko" so he could view it, and called Moore "chicken" for canceling.
"Guess he didn't expect anyone to seriously take him on," DeLay wrote on his Web site. "Had I known he was this chicken, I would have accepted on the spot, but at least I can spare myself the agony of watching one of his mockumentaries. Bottom line: his movies, his politics, and his incessant bullying are all an act."