Image copyright Madonna / Instagram Image caption The low-key show was only open to fans who entered a competition on Madonna's website

Pop star Madonna has spoken emotionally about her estranged son, Rocco, at her first Australian show in 23 years.

The singer wiped away tears as she discussed her custody battle with ex-husband Guy Ritchie, and dedicated the song Intervention to Rocco.

Pictures of the 15-year-old were projected behind the star as she sang.

The performance was part of an intimate one-off show at The Forum in Melbourne; which was only open to 1,500 competition winners.

Called Tears Of A Clown, it presented the star as a confessional singer-songwriter (albeit one dressed in a circus outfit), as she ditched her dancers and dissected her most personal songs.

They included Mer Girl, from the album Ray of Light, which Madonna said was inspired by visiting her mother's grave and finding it covered in weeds.

Image copyright Getty Images Image caption The ramshackle show allowed fans a much more intimate look at the star, whose tours have become known for their lavish set-pieces and intricate choreography

The show started three hours late after rehearsals over-ran, leaving fans - some of whom had been queuing since Monday - waiting outside in the pouring rain.

But when she finally took to the stage, shortly after midnight, Madonna received an enthusiastic response from the audience, who shouted "we love you" and "you're the queen" as she trundled around the stage on a tricycle.

The star repeatedly insisted Tears Of A Clown was "brand spankin' new" and a "work in progress".

"I want to make a disclaimer," she said. "If anyone thinks they came here to see a finished final show, there's the door."

'Mistakes'

Her tribute to Rocco came seven songs into the set.

"There's no end to the mistakes I've made," she said. "Everybody knows the saga of me and my son Rocco. It's not a fun story to tell or think about.

"I probably could have enjoyed myself a little bit more on this tour if he hadn't disappeared so suddenly, and also if I knew when I would see him again. I want to dedicate this next song to him, to Rocco."

The song, from the American Life album, opens with the lyrics: "I've got to save my baby / Because he makes me cry / I got to make him happy / I got to teach him how to fly."

Image copyright Tony Villanueva / Instagram Image caption Madonna fan Tony Villanueva posted a picture of the setlist on Instagram

The setlist included covers of Stephen Sondheim's Send In The Clowns and Elliot Smith's Between The Bars; alongside fan-favourite tracks like Take A Bow, Don't Tell Me and I'm So Stupid, the latter of which had never been performed live before.

Between the songs, Madonna exchanged banter with the crowd, reflected on her past relationships and told jokes - both lewd and hackneyed. "Do you guys know how you kill a clown?" went one. "You go for the juggler".

But, aside from a ukulele version of Holiday, which closed the show, the music was sombre and melancholy.

Madonna explained she had chosen a clown theme for the show because "to me they symbolise heartbreak. There's something tragic about clowns because they try so hard to make you laugh, to make you smile."

"They are obviously covering up something, there is something going on inside. What do you think is going on inside of me?"

The show, at Melbourne's Forum Theatre, took place hours after a hearing took place in London's High Court to resolve a custody dispute between Madonna and her former husband, film director Guy Ritchie.

The couple, who divorced in 2008, are negotiating over the future of their son, who left Madonna's world tour and moved in with his father late last year.

The hearing continues on Friday.