The war of words blew up when O'Connor wrote to the former Hannah Montana singer warning her not to over sexualise her public image, but Cyrus hit back on Twitter.com with a veiled reference to O'Connor's mental health issues, comparing her to troubled actress Amanda Bynes.
She also reminded her followers of the controversial 1992 incident when O'Connor ripped up a picture of Pope John Paul Ii on live Tv.
Now the furious Nothing Compares 2 U singer has penned a third open letter to the Wrecking Ball hitmaker demanding a public apology over her catty remarks and snubbing her offer of a meeting.
O'Connor writes, "You can take five minutes today between g-string f**kin' changes to publicly apologise and remove your abusive tweets. If you do not then you don't give a s**t who you mock and what damage you do by being so ignorant. When you publicly apologise to Amanda and myself and all mental health sufferers as well as all who were abused by priests that will end the matter as far as I am concerned."