SAME-SEX marriage advocates are hoping Tony Abbott will listen to his daughters and change his blanket opposition to gay marriage.

Frances and Bridget Abbott have told News Limited they believe same-sex couples should be able to marry and have discussed the matter with their father.

Their stance has buoyed gay marriage advocates, who have also welcomed the support of Melbourne's Liberal Lord Mayor Robert Doyle on the issue.

The former Victorian Liberal Party leader on Saturday used Twitter to support marriage equality, and urged others to join him.

"Let's show the world where we stand as a city," Cr Doyle tweeted.

Australian Marriage Equality national director Rodney Croome says the pressure is growing on Mr Abbott to change his opposition to gay marriage.

"Frances and Bridget Abbott's support for marriage equality reflects strong support for the issue among young Australians," Mr Croome said in a statement.

"We hope their stance ... will encourage Tony Abbott to evolve on the issue, at least by allowing coalition MPs a conscience vote."

Mr Abbott's two youngest daughters said their views were shaped by seeing their aunt, Mr Abbott's sister, fall in love with a woman.

Mr Abbott recently said his views on homosexuality had changed and he now warmly accepted his sister, Christine Forster, as a lesbian after she left her marriage of 19 years to be with her new partner, Virginia Edwards.

Australian Marriage Equality meanwhile hopes Mr Doyle's stance will also influence Liberal voters nationwide.

Mr Croome said the Melbourne mayor supported gay marriage because he believed in individual freedom from government interference - an argument many Liberal Party MPs and voters would wholly support.

Originally published as Abbott under pressure on gay marriage