Minaj was recently seen shouting at fellow judge Carey in leaked footage from auditions, and Nicks later made controversial comments about the row.
"How dare this little girl!" she told The Daily. "If I had been Mariah I would have walked over to Nicki and strangled her to death right there."
However, Nicks has now expressed regret for her comments in a statement to the New York Daily News.
"I want to apologise for my remarks about Nicki Minaj's behaviour toward Mariah Carey which I said during a long and exhausting day of interviews," she said.
"It was very out of character for me and I deeply regret what I said. I feel very protective toward Mariah Carey, who has gone through many difficulties in her life, and I spoke without thinking."
Nicks added: "I think all artists should be respectful toward one another and that includes me. I am truly sorry."
American Idol bosses recently attempted to play down the reported feud between Carey and Minaj by insisting that "production is going extremely well".