(CNN) An LGBT group has cut ties with tennis great Martina Navratilova after she said it was a form of "cheating" for transgender women to be allowed to compete in women's sport.

New York-based Athlete Ally, which supports LGBT sportspeople, called the comments transphobic and removed the 18-time Grand Slam winner from its advisory board and as an ambassador.

Navratilova wrote in The Sunday Times that it was "insane" that transgender athletes who "decide" to become female had achieved honors "that were beyond their capabilities as men."

"Martina Navratilova's recent comments on trans athletes are transphobic, based on a false understanding of science and data, and perpetuate dangerous myths that lead to the ongoing targeting of trans people," Athlete Ally said in a statement

"Trans women are women, period. They did not decide their gender identity any more than someone decides to be gay, or to have blue eyes," the group added.

"They are women, and want to compete in the sport they love, just as any other athlete would."

The move follows a flurry of criticism directed at Navratilova, a gay rights campaigner who herself suffered homophobic abuse when she came out in 1981, for her Sunday Times column.

Navratilova, who competed for Czechoslovakia and the United States, wrote that "it would not be fair" if she had to play against a transgender woman.

But trans rights group Trans Actual responded on Twitter: "We're pretty devastated to discover that Martina Navratilova is transphobic. If trans women had an advantage in sport, why aren't trans women winning gold medals left, right & centre?"

"Trans women don't have an advantage. Look up the changes that oestrogen makes to the body," they added.

Navratilova has defended her comments, tweeting to CNN on Tuesday that the controversy is "not about me and it is not about whether I was criticized or not -- you ought to talk about the actual issues I raised instead."

According to current rules issued by the International Olympic Committee in 2016, trans men are allowed to compete without restriction.

Trans women, however, must show that their testosterone level has been below a certain level for at least 12 months before their first competition.

'Irrational fear'

Navratilova has caused controversy for her comments on transgender athletes before.

In December she was criticized after tweeting: "You can't just proclaim yourself a female and be able to compete against women. There must be some standards, and having a penis and competing as a woman would not fit that standard."

Those comments led to her becoming embroiled in an online argument with cyclist Rachel McKinnon, the first transgender woman to win a world track cycling title in October 2018.

Athlete Ally said it had reached out to Navratilova after that incident but had not heard back.

"We believe that growth is possible, and we extend once again to Martina the invitation to learn from this experience," the group said Tuesday.

McKinnon reacted to Navratilova's latest comments by tweeting: "It's a wild fantasy worry that is an irrational fear of something that doesn't happen. An irrational fear of trans people? Transphobia."

This is, in her own words with the time of forethought and authorship, Martina Navratilova's 'core' argument against trans women athletes.



It's a wild fantasy worry that is an irrational fear of something that doesn't happen. An irrational fear of trans people? Transphobia. pic.twitter.com/RAX3ynGyTl — Dr. Rachel McKinnon (@rachelvmckinnon) February 17, 2019

Navratilova rejected accusations of transphobia, adding that she deplores "what seems to be a growing tendency among transgender activists to denounce anyone who argues against them and to label them all as 'transphobes.'"

She also highlighted her friendship with Renée Richards, the transgender tennis player who campaigned to be able to play in the women's US Open.