He told ABC News' John Quinones on "Primetime Live" he knew it was wrong. "That's why we were keeping it secret," Clark said.
Abdul picked his songs and took him shopping, paying for his clothes, reports The Early Show national correspondent .
Abdul denies Clark's assertions, saying, "I won't dignify it by even talking about it."
Fox, on which "Idol" airs, says it will "of course, look into any evidence of improper conduct," adding that the public should "carefully examine Mr. Clark's motives."
Clark is trying to sell a CD, but says he's going public with the affair to move on with his life.
"I'm just cleaning up my own pathway, you know what I'm saying, if that involves getting your dirt off my pathway, I got to do it," he said on "Primetime Live."
Two years ago, Clark was dropped from the competition because he hadn't disclosed a previous arrest. In the newest issue of People magazine, he blames Abdul for not coming to his defense at the time, saying, "She left me hanging high and dry."
Now, he's releasing a song called "Paula-tics," about their secret romance.
Clay Aiken, himself a contestant on "American Idol" when Clark was, tells The Early Show co-anchor Rene Syler he finds Clark's story .
But Entertainment Weekly TV Editor Lynette Rice says, "There is obviously proof, phone records, multiple phone records. …He went out in public with her. This warrants at least a discussion between the network and the producers, you know, 'Do we have a problem here?' "
Kauffman asked "Celebrity Justice" executive producer if this amounts to a scandal, or a legal problem.
"I think it's a scandal," he answered. "Nobody's going to get prosecuted for this. I think it's highly embarrassing for Paula Abdul."
Adding to the embarrassment, Kauffman notes, one line in particular in Clark's tell-all song: "A secret's not a secret when it's no longer secret, straight up."
Abdul got a standing ovation on Wednesday night's "American Idol," when the remaining contestants gave her flowers.