NEW YORK (AFP) - David Bowie's family said on Thursday it planned a private ceremony to celebrate the late rock legend as it kept details around his shocking death under guard.

"The family of David Bowie is currently making arrangements for a private ceremony celebrating the memory of their beloved husband, father and friend," said a statement on Bowie's official Facebook page.

"They ask once again that their privacy be respected at this most sensitive of times.

"We are overwhelmed by and grateful for the love and support shown throughout the world."

Bowie, one of pop culture's most influential figures whose career took him from glam rock to science fiction movies to jazz, died on Sunday after an undisclosed 18-month battle with cancer.

Few other details have emerged.

Representatives for the London-born artist declined comment on a report in Britain's Daily Mirror that said that his body was cremated in New York, his adopted home, immediately after his death.

People close to him said that Bowie wanted to keep his illness away from the glare of 24-hour social media.

He instead released a final album, Blackstar, on his 69th birthday on Friday in what in retrospect was an elaborate artistic statement on his death and nearly half-century career.

In the words of photographer Annie Leibovitz, "he really curated his death."

Bowie's death has triggered an outpouring of mourning, with fans around the world leaving flowers, candles and glitter on sites associated with the outwardly flamboyant but also meditative artist.

"It is important to note that while the concerts and tributes planned for the coming weeks are all welcome, none are official memorials organised or endorsed by the family," the Facebook statement said.

"Just as each and every one of us found something unique in David's music, we welcome everyone's celebration of his life as they see fit," it said.