Germaine Greer has accused TV star Caitlyn Jenner of stealing the limelight from other female members of the Kardashian family, in comments likely to further alienate campaigners who object to the writer and commentator’s views about transgender people.

The Australian-born writer courted controversy in an interview with BBC2’s Newsnight by claiming that “misogyny played a big part” in the rumoured decision by Glamour magazine to give Jenner its woman of the year award.

Jenner, who was born Bruce, was married to Kris Jenner, Kim Kardashian’s mother, until they filed for divorce early last year.

She also refused to back down from her position that transgender women, who have begun life as men before undergoing surgery and hormone treatment to become women, are “not women”, saying they do not “look like, sound like or behave like women”.

Greer was speaking after it emerged that an online petition had been launched seeking to prevent her giving a lecture at Cardiff University. The organisers claimed her views were “problematic” for transgender people.

Asked to address the issue of Jenner being tipped for woman of the year, as reported earlier this week, Greer said: “I think misogyny plays a really big part in all of this, that a man who goes to these lengths to become a woman will be a better woman than someone who is just born a woman.”

“It seems to me that what was going on there was that he/she wanted the limelight that the other, female, members of the family were enjoying and has conquered it, just like that,” she added, snapping her fingers.

The petition on Change.org, which was started by Rachael Melhuish, women’s officer at Cardiff University students union, alleged that Greer has “demonstrated misogynistic views towards trans women, including continually misgendering trans women and denying the existence of transphobia altogether”.

It adds: “While debate in a University should be encouraged, hosting a speaker with such problematic and hateful views towards marginalised and vulnerable groups is dangerous. Allowing Greer a platform endorses her views, and by extension, the transmisogyny, which she continues to perpetuate.”

By Saturday afternoon it had been signed by more than 800 people.

Greer has maintained her position on transgender women,saying: “I’m not saying that people should not be allowed to go through that [sex change] procedure. What I’m saying is that it doesn’t make them a woman. It happens to be an opinion. It’s not a prohibition.”

Addressing claims that she had been hurtful towards transgender women, Greer added: “People are being hurtful to me all the time. Try being an old woman. For goodness sake, people get hurt all the time. I’m not about to walk on eggshells.”

Greer, author of The Female Eunuch, a classic on women’s sexuality, had been due to speak on 18 November in a lecture called Women & Power: The Lessons of the 20th Century. She has now said she will not make the speech if the university cannot guarantee she “will not have things thrown” at her.

Asked about the petition, she told the Guardian on Friday: “I don’t really know what I think of it. It strikes me as a bit of a put-up job really because I am not even going to talk about the issue that they are on about.

“What they are saying is that because I don’t think surgery will turn a man into a woman I should not be allowed to speak anywhere.”