American pop star Lady Gaga has been declared an honorary citizen of Sydney for her 'unwavering support' of gay rights as she delighted fans with surprise shows at two city nightspots, the Agence France Press reports.

The cryptic pop diva was given the honour during a low-key tour of Sydney, which will feature just one invite-only concert at the city's Town Hall for 1,000 people, as a token of gratitude for her gay rights work.

"Lady Gaga has been a powerful force for the gay and lesbian community in Sydney, and we have a rare honour for people whose achievements embrace the ideals and spirit of our city - the title of 'Honorary citizen of Sydney," said Lord Mayor Clover Moore on Tuesday.

Mr Moore said the award paid tribute to the artist's use of her 'star power to focus the world's attention on the prejudice still directed at gay men and women.

Despite being among the world's gay and lesbian capitals - annually hosting the renowned Mardi Gras gay pride march - Mr Moore said Sydney's same-sex couples were still denied the right to marry under national law.

"The law needs to change. Every Australian who wants to make a life commitment to the person they love should be able to do so. And have that commitment equally recognised and supported by the law," Lady Gaga said at the press event.

Born Stefani Germanotta, Lady Gaga used an interview on prime time television Monday night to call for Australian Prime Minister Julia Gillard to legalise same-sex marriage.

"I am so against the way certain laws and restrictions send messages that one person is better than another," she told the Nine Network. "I urge all of you to mobilise your voices so the prime minister can hear you scream that you want to be equal."