"The message you keep sending is that it's somehow cool to be prostituted.. it's so not cool Miley... it's dangerous," commented O'Connor.
"It is in fact the case that you will obscure your talent by allowing yourself to be pimped, whether it's the music business or yourself doing the pimping," added O'Connor.
Responding on Twitter, Cyrus wrote: "Top of the mornin to ya."
She added a screen shot of O'Connor's tweets from 2012 in which the Irish star, who has bi-polar disorder, referred to her own mental health problems, asking for Twitter followers to recommend a psychiatrist.
She also compared the singer to former child actress Amanda Bynes, who is currently undergoing psychiatric treatment.
Irish singer Sinead O'Connor is unhappy with Miley Cyrus' overtly sexualised stage performances
Responding to Cyrus in a third open letter, O'Connor said she would take legal action against her if she did not remove the tweets.
"You have posted today tweets of mine which are two years old, which were posted by me when I was unwell and seeking help so as to make them look like they are recent.
"In doing so you mock myself and Amanda Bynes for having suffered with mental health issues and for having sought help.
"It is most unbecoming of you to respond in such a fashion to someone who expressed care for you," O'Connor added.
"And worse that you are such an anti-female tool of the anti-female music industry."
The row began after Cyrus claimed in Rolling Stone magazine that the video for her Wrecking Ball song was modelled on O'Connor's Nothing Compares 2 U, where she sheds a single tear.
However, O'Connor expressed concern that the former child star was being exploited, with the video also showing her licking a sledgehammer and writhing naked on a swinging metal demolition ball.
The 46-year-old said: "I am extremely concerned for you that those around you have led you to believe, or encouraged you in your own belief, that it is in any way 'cool' to be naked and licking sledgehammers in your videos."
Watch the video for Miley Cyrus's Wrecking Ball on YouTube, below:
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