In her first letter, the 'Nothing Compares 2 U' hit maker had asked the former Disney star to resist music industry's pressure to "prostitute" herself, Stuff.co.nz reported.
While replying to O'Connor's public letter via Twitter, the 'We Can't Stop' singer compared O'Connor with troubled actress Amanda Bynes, who has recently been in psychiatric care.
Along with the tweet, Cyrus posted a screen grab of O'Connor's Twitter feed from 2012, which showed the 46-year-old star asking for help from a psychiatrist.
In her second letter, O'Connor asserted that the screen shots shared by Cyrus earlier were posted by her when she was not well and seeking help.
O'Connor added that Cyrus' tweets mock her and Bynes for having suffered with mental health issues and for having sought help.
--ANI (Posted on 04-10-2013)