Image copyright Reuters Image caption The star died of cancer on Sunday, aged 69

David Bowie's family have said they are "overwhelmed" by the global tributes that have been paid to the singer since his death.

A statement on Bowie's Facebook page also said they were arranging "a private ceremony" in his memory.

They also welcomed the concerts and tributes that have been planned, but pointed out they were not officially endorsed.

Bowie died of cancer on Sunday, aged 69.

According to reports. the singer's body has been privately cremated in New York. In line with his wishes, no family or friends were present at the ceremony, the Daily Mirror reported.

A publicist for the singer told the BBC they were "neither confirming nor denying" the story.

The family statement on Thursday, titled "Thank you", said: "The family of David Bowie is currently making arrangements for a private ceremony celebrating the memory of their beloved husband, father and friend.

"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.

"However, it is important to note that while the concerts and tributes planned for the coming weeks are all welcome, none are official memorials organized or endorsed by the family. 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."

Bowie had released a new album, Blackstar, just two days before his death, which has been retrospectively interpreted as his epitaph.

Although the record features lyrics such as "Look up here, I'm in heaven," its producer Tony Visconti said the star had written and demo-ed five new songs in recent weeks.

Image copyright AFP / Getty Images Image caption The singer's cancer had been in remission until last November, Visconti told Rolling Stone

Speaking to Rolling Stone magazine, Visconti said Bowie had called him about a week before his death and "at that late stage, he was planning the follow-up to Blackstar".

"I was thrilled," said the producer, who worked on key Bowie albums including The Man Who Sold the World, Low and 2013's surprise comeback The Next Day.

"I thought, and he thought, that he'd have a few months, at least. So the end must've been very rapid. I'm not privy to it. I don't know exactly, but he must've taken ill very quickly after that phone call."

Visconti will be one of the musicians performing at a memorial concert for Bowie at New York's Carnegie Hall in March.

The Music of David Bowie had originally been billed as a tribute show, with artists including Cyndi Lauper and The Roots also performing, but the event will now give fans the opportunity to mourn.

Tributes will also be paid at next month's Brit Awards, with a performance celebrating the "extraordinary life and work of one of our greatest icons".

Meanwhile, Blackstar is set to become Bowie's first number one album in the US, as sales surged after news of his death broke on Monday.

The critically acclaimed record is also headed to number one in the UK, while 13 of his previous albums are expected to enter the top 100.

Watch a special tribute programme David Bowie: Sound and Vision on the BBC iPlayer