Joan Rivers remains on life support, the comedienne's daughter, Melissa Rivers, said in a statement released Tuesday afternoon.
"On behalf of my mother and our family, we are extremely grateful for all the love and support we've received. At this time she does remain on life support," she said. "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."
According to earlier reports, Rivers was slowly being taken out of a medically induced coma.
The 81-year-old TV personality was rushed to New York's Mount Sinai Hospital last Thursday when she suffered cardiac arrest after her breathing stopped during a procedure at a Manhattan doctor's office.
On Sunday, Melissa Rivers said, "Thank you for your continued love and support. We are keeping our fingers crossed."
The day before, Rivers said her mother's condition "remained serious."
Melissa Rivers previously released a statement, saying, "I want to thank everyone for the overwhelming love and support for my mother. She is resting comfortably and is with our family. We ask that you continue to keep her in your thoughts and prayers."
Joan Rivers was in New York getting ready to tape her E! television series, "Fashion Police," to coincide with New York Fashion Week.