The pair exchanged heated words on last night's live show after Walsh claimed that his fellow judge had "stolen" a song that he wanted to secure for his boyband JLS. The track in question, Take That's 'Rule The World', was given to Rachel Hylton as Minogue had first choice as part of a rota system drawn up between the mentors.
After the ITV1 programme returned from a commercial break, Minogue had broken down in tears and was unable to introduce Hylton's performance.
Speaking later on ITV2 spinoff The Xtra Factor, Simon Cowell insisted: "Dannii did exactly what I would do, which is choose the right song for the artist and if Louis doesn't like it, tough!
"There's no point pointing fingers at Dannii saying that she stole the song. She didn't steal the song, she had the right to choose that song and [she] did the right thing for Rachel. Next week, we change the order again - that's the way it goes."
Earlier this month, Minogue admitted that she was trying to put on a brave face after receiving "taunts" in the press this year.
Asked for her take on the argument, Hylton said: "Leave Dannii alone. It was a rota system. I think it's really unfair that you keep having these bad jibes at me and my mentor. It's not on. We're people and we've got feelings too. I just want people to leave my mentor alone - she's a lovely woman."
The programme's host Holly Willoughby added: "She is a lovely lady and she's strong as well. I think the good thing about tonight is that no one thinks Dannii was in the wrong."