The singer broke down in tears in last night's live show after Walsh claimed that she had "stolen" a song that he had hoped to secure for boyband JLS.
Minogue's act Rachel Hylton was permitted to perform Take That's 'Rule The World' despite Walsh's wishes because the Aussie popstar had the first choice of songs this week.
Responding to Walsh's accusation, an emotional Minogue insisted: "I would never, ever steal anyone else's song. I had the absolute right to choose that."
Speaking later on The Xtra Factor, the star claimed that Walsh was trying to "trip [her] up" by giving a misleading account of her behaviour.
She told show host Holly Willoughby: "All I'm doing is my job for the act. It stinks."
Minogue has been backed by Simon Cowell following the argument. The music mogul said: "Dannii did exactly what I would do, which is choose the right song for the artist and if Louis doesn't like it, tough!"