"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."
"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," she added.
Melissa's statement follows reports that her mother would be taken off life support. Joan has been in a medically induced coma since going into cardiac and respiratory arrest while undergoing a scheduled throat surgery on Thursday.
The 81-year-old comedian was rushed to Mount Sinai Hospital in New York City from the outpatient facility and has remained there ever since. Melissa's previous update on her mother's condition claimed the E! star was "resting comfortably" and thanked fans for "the overwhelming love and support for my mother."