Movie icon Marilyn Monroe was naked underneath the famously form-fitting dress she wore while singing a flirty "Happy Birthday, Mr. President" to then US leader John F. Kennedy, according to a new book.

The late movie star serenaded the tragic President at a Democratic Party fundraiser in New York City a few days ahead of his 45th birthday in May, 1962, fuelling rumours suggesting she was having affairs with both Kennedy and his brother Robert, reports aceshowbiz.com.

Late director Mike Nichols shared a secret from beyond the grave in the just-published "Life Isn't Everything: Mike Nichols, As Remembered By 103 Of His Closest Friends," by Ash Carter and Sam Kashner. The book comprises tales the "Who's Afraid of Virginia Woolf?" filmmaker shared with friends and acquaintances before he died in 2014.

Monroe's story in the book comes from New York Times columnist Maureen Dowd, who told the book's writers, Ash Carter and Sam Kashner, what her friend relayed about the evening.

"When Marilyn sang Happy Birthday to Jack Kennedy in the famous dress she had to be sewn into, the sequined Jean Louis (designer) gown, Mike was there that night," she remembered.

"He told me, 'I was standing right behind Marilyn, completely invisible, when she sang Happy Birthday, Mr. President, and, indeed, the corny thing happened. Her dress split for my benefit, and there was Marilyn, and, yes, indeed, she didn't wear any underwear'."

Monroe died less than three months later, aged 36, of a drug overdose, while President Kennedy was assassinated the following year.