"We're professionals. Have you ever had an argument with someone you've worked with?" Minaj said after repeated questions Tuesday about her reported feud with new fellow judge Carey.
"This was sort of one-sided," interjected Carey, wearing a queenly smile.
"No, it wasn't," snapped back Minaj.
Fox network executive Mike Darnell was asked by reporters with the Television Critics Association if the clash was authentic. He said there was a lot of musical passion within the group, which also includes country star Keith Urban and returning judge Randy Jackson, and that triggered disagreements.
"The fighting is what it is," Carey said at one point. "This is 'American Idol.' It's bigger than all that. It's bigger than some stupid trumped-up thing."
Reports that the two divas were at odds surfaced last fall. On "The View," Barbara Walters recounted a phone conversation with Carey in which the pop star said that Minaj threatened to shoot her after a taping. The rapper quickly responded with dismissive tweets.
Trumped up or not, she and Minaj appeared on the panel with Urban carefully placed between them and indulged in their briefly testy "one-sided" exchange. But they also responded to a request to say something nice about each other.
Minaj called Carey one of her favorite all-time artists who has shaped a generation of singers. In return, Carey fondly recalled working with Minaj on a single titled - "ironically," as Carey noted - "Up Out My Face."
"I knew she was going to go far, and still is," Carey said.
"American Idol" begins its 12th season Wednesday facing questions once again about its ability to endure as a top-rated show, especially given the increasingly crowded talent show landscape that includes NBC's hit "The Voice." All the shows are down in the ratings, Darnell noted.
Veteran executive producer Nigel Lythgoe is used to hearing the query. Famous judges have the pre-debut spotlight and media attention but the contestants ultimately are what keep viewers watching, he said after the panel.
That's not to say the panel isn't key, said Trish Kinane, another executive producer.
"We wanted judges who were experts and had a right to be here, and we also wanted honesty," she said. "We very much took that into consideration. I think we've got it. They're not shrinking violets, they say what they think, and we encourage that."
Minaj displayed that Tuesday, saying firmly that "Idol" is not the show for rap, her own genre.
"If you're looking for people to believe you and feed you as a rapper, I wouldn't do it," said Minaj, adding that viewers love "American Idol" as an "honest singing competition, and I'm not here to change that."