“I think people should be allowed to have the male to female procedure… all I’m saying is that it doesn’t make them a woman,” she said in an interview with BBC Newsnight.
She also claims that “a great many women” who are not transgender think transgender women – who she refers to as “male to female transgender people” – do not “look like, sound like or behave like women”.
Her comments have prompted an outburst, with critics saying she should “keep quiet” on the issue.
Greer did say that she would be prepared to use female pronouns when referring to someone if that was their preference, “as a courtesy”.
A petition has been launched asking Cardiff University to cancel a lecture by Germaine Greer, saying her views are “problematic” for transgender people.