Equality groups have lashed the Perth Lord Mayor after he made comments about transgender on breakfast radio that were "repugnant and bigoted".

Basil Zempalis told listeners that it was "wrong" for someone to identify as a different gender to their physical anatomy.

"If you've got a penis mate, you're a bloke," he said yesterday morning.

"If you've got a vagina, you're a woman. Game over."

His co-host Steve Mills pointed out that he would likely meet transgender people in his role as Lord Mayor, which Zempalis laughed off.

Zempalis then made a public declaration for any woman with a penis to ring in the radio station for a chance to win a $100 store voucher.

After being warned by Mills that people in the wider community might not like his stance, Zempalis shrugged it off.

"Well mate, if you want to go softy, lefty, namby-pamby," he said.

TransFolk WA chair Hunter Gurevich sai that Zempilas' comments were harmful to transgender people.

"These comments are repugnant, bigoted, narrow-minded, parochial and fundamentally deny contemporary science," he said.

"Further, it puts LGBTQIA+ people at increased risk of harm, when we are already a vulnerable group in society."

Pride WA president Curtis Ward said that the comments were misinformed and damaging.

"It is possible to appear one way and feel another and when someone says they're transgender, they are simply saying they feel differently to how they appear," Mr Ward said.

"[That is] sex being your physical appearance and your biology whereas gender is how you identify psychologically, whether you're feminine or masculine."

"I think people need to be educating themselves about what they're speaking about and if they do have that stage, and they are commanding such a large audience, they should be making educated statements," he said.

Zempilas has since issued an apology for his remarks.

"The comments were inappropriate and I apologise. It was early morning radio banter gone wrong," he said in a text message.

"The comments do not reflect how I feel. I did not intend to cause any offence and I am sorry. It will not happen again."

He spoke on his radio show 24 hours after the incident, saying that the comments were a "bad mistake".

"What's more disappointing is that I understand that that is indeed how people live their lives … I was aware of that yesterday," he said.

"Those comments don't reflect my values, they don't reflect the values of 6PR or Channel 7, they don't reflect the values of the City of Perth.

"I had a very strong talking to from my wife last night. They don't represent her values. Her best friend is gay."

He urged listeners that he would learn from his mistake.

"All you can do in life is go, 'I made a blue, I'm sorry,' and you've got to try not to do it again, and that's exactly what I'll do," he said.

"I have to get better and I will get better."