Melissa Rivers has reached out to fans with an update on her mother Joan Rivers' condition.
"On behalf of my mother and our family, we are extremely grateful for all the love and support we've received," Melissa said in a statement. "At this time, she does remain on life support.
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Joan Rivers remains on life support, her daughter Melissa Rivers has confirmed
"I know my mother would be overwhelmed by the continued outpouring of kindness, and I want to thank everyone for keeping us in their prayers."
Melissa has been keeping a vigil by her mother's bedside as she continues to receive treatment at New York's Mount Sinai Hospital.
The 81-year-old was admitted last Thursday after she stopped breathing during surgery on her vocal chords at a private Manhattan clinic.
Joan Rivers stopped breathing during surgery on her vocal chords last week
On Sunday, doctors began the process of lifting Joan out of a medically induced coma. Melissa said she remained hopeful of a recovery – there are fears that the star could be left with permanent brain damage or in a wheelchair.
Joan had shown no signs of illness in the days prior to her operation, recording scenes for Fashion Police and performing gigs as part of her current North America tour.