Minaj and Carey were seen in a leaked video apparently clashing with each other during auditions in Charlotte, North Carolina on Tuesday (October 2), which apparently stemmed from a contestant's performance.
Seacrest, who was outside the audition room during the spat, shared on his radio show On Air With Ryan Seacrest: "It got heated between Nicki and Mariah. It was intense! I'll be honest with you... It went far last night. It did get intense."
In the video clip, Minaj appeared visibly angry with Carey, telling her: "I told them, I'm not f**kin' putting up with her f**kin' highness over there."
The Idol host went on to say: "These are all very different individuals with different perspectives and different opinions that provide for interesting conversation and dialogue and feedback for the contestants."
Seacrest added that disagreements on the programme are "gonna happen, and it's okay".
"We want that! We want them to be on this panel together," he said. "This is a good team, a great team, to go out and look for the next American Idol... the feedback that they give is very good."
The American Idol judging panel also includes country star Keith Urban and long-time judge Randy Jackson.
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Watch video of Nicki Minaj's reported outburst at Mariah Carey on the American Idol set below: