The comedian and TV presenter Joan Rivers has died at the age of 81, a week after becoming ill during a hospital procedure.

The co-star of TV show Fashion Police had been on a life support machine at the Mount Sinai hospital in New York last week. She had suffered a cardiac arrest, having stopped breathing during a procedure on her vocal chords at a clinic in the city a week ago.

Her death was announced last night in a statement issued by her daughter Melissa. She was surrounded by her family at her bedside.

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In a statement, she said: "It is with great sadness that I announce the death of my mother, Joan Rivers.

"She passed peacefully at 1.17pm surrounded by family and close friends. My son and I would like to thank the doctors, nurses, and staff of Mount Sinai Hospital for the amazing care they provided for my mother."

Mrs Rivers said she and her son Cooper, 11, were "humbled by the outpouring of love, support and prayers we have received from around the world."

"My mother's greatest joy in life was to make people laugh," she added. "Although that is difficult to do right now, I know her final wish would be that we return to laughing soon."

Tycoon Donald Trump, tweeted of the stand-up comedian: "Joan Rivers was an amazing woman and a great friend. Her energy and talent were boundless. She will be greatly missed."

Lord Sugar , the star of the BBC TV's Apprentice, said the death was "very sad news" and described her as a "great character".

Actress Emma Freud, tweeted: "The ultimate yenta... The quintessential kibitzer'. Goodbye Joan Rivers." Bafta called her death "sad news".

Rivers had been on life support for almost a week and there had been no ­information regarding her prognosis.

She was a favourite with Fashion Police viewers for her caustic comments about the clothes worn by the rich and famous.