The feud began when Kelly Osbourne called GaGa's fans "the worst", claiming that she has received death threats from them.
GaGa replied with an open letter, suggesting that the reality star's work on E!'s Fashion Police "breeds negativity" and encourages people to be judgemental. She also urged Kelly to "take responsibility and accountability".
"It used to make me truly sad when I would hear people talk about your weight when you were younger, as I was bullied too. To see you blossoming into a beautiful slender woman who makes fun of others for a living is astounding. Why not help others?" she said.
Sharon then stepped in, branding GaGa a "[publicity-]seeking hypocrite" and "a bully" over her criticism of Kelly. She also called GaGa's letter "full of contradictions" and said it should have remained private.
"You say her work on E! with the Fashion Police is 'rooted in criticism, judgment, and rating people's beauty against one another'. Welcome to the real world," she said.
GaGa has since addressed the incident on Facebook, saying: "The 'real world' can be cruel, why not try to change it into a better place? I am an activist. Nobody takes adolescents seriously, I do.
"My letter to Kelly Osbourne was open, because her statements on cyber-bulling were public & as a youth activist I'm compelled to be involved."
Osbourne previously said that GaGa "really has created monsters" in reference to the singer's nickname for her fans.
Photo gallery - GaGa's most eccentric moments so far:
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