Equality groups have branded comments the Perth Lord Mayor made about transgender people on breakfast radio "repugnant and bigoted".

Basil Zempilas, who was elected to office earlier this month, told listeners of the breakfast show he co-hosts on 6PR 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."

Mr Zempilas then laughed off a suggestion by co-host Steve Mills that he would likely come into contact with transgender people in his role as Lord Mayor.

Mr Zempilas also called for any women with a penis to ring the radio station for the chance to win a $100 store voucher.

When Mr Mills suggested that people in the wider community may disagree with his stance, Mr Zempilas replied: "Well mate, if you want to go softy, lefty, namby-pamby."

The pair had been discussing an LGBTIQ boxing tournament in Sydney, which led to a debate about parents who did not identify their children as male or female.