Cyrus and O'Connor became embroiled in an online feud last week (ends06Oct13) after the Irish singer posted an open letter to the former Hannah Montana star warning her not to over-sexualize her public image.
Cyrus responded on Twitter.com by mocking O'Connor's mental issues and comparing her to troubled actress Amanda Bynes.
The feud further escalated with O'Connor threatening legal action, while Cyrus insisted the two women should meet up to discuss their issues.
But Miley was keen to point out that she remains a big admirer of the Irish star's work during an appearance on U.S. breakfast show Today on Monday (07Oct13), stating, "I think she's an incredible artist, an awesome songwriter and I was really inspired by her for my Wrecking Ball video, which is what started the whole thing.
"I don't know how someone can start a fight with somebody who's saying, 'Hey, I really respect you and I really love what you did'."
O'Connor was clearly upset when Cyrus made it clear that her provocative promo, in which she swings about naked on a chained metal wrecking ball, was inspired by the Irish singer's Nothing Compares 2 U video.
Cyrus explained she can't understand why O'Connor would attack her and suggest that she was being "exploited".
She added, "That was kind of crazy, but, like I said, I'm a big fan of hers, so it doesn't really matter."