(CNN) -- Joan Rivers remains on life support five days after suffering respiratory and cardiac arrest during a medical procedure, her daughter said Tuesday.
Melissa Rivers has shared few details with the public about her mother's condition since she was rushed to Manhattan's Mount Sinai Hospital Thursday.
"On behalf of my mother and our family, we are extremely grateful for all the love and support we've received," she said in her latest 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."
The Rivers family's previous statement Sunday said they were "keeping our fingers crossed."
The Cleveland Clinic explains what being on life support means: "Life support replaces or supports a failing bodily function. When patients have curable or treatable conditions, life support is used temporarily until the illness or disease can be stabilized and the body can resume normal functioning. At times, the body never regains the ability to function without life support."
Rivers, 81, stopped breathing during throat surgery at a Manhattan medical clinic Thursday morning, according to the New York Fire Department. She apparently suffered cardiac and respiratory arrest during a procedure. She was listed in critical condition in New York's Mount Sinai Hospital, where paramedics took her by ambulance.
Rivers was undergoing an apparently minor elective procedure at the clinic, which is about a mile away from the hospital where she was taken.
Despite her age, Rivers was a busy comedian.
She had been scheduled to tape new episodes of the E! show "Fashion Police" with her daughter in New York this week, but the tapings have been canceled, a network spokeswoman said.
She performed her comedy act at New York's Laurie Beechman Theatre last Wednesday night and was booked to perform at the Count Basie Theater in Red Bank, New Jersey, on Friday.
Michael Lucas, who was in the audience for Rivers' last show Wednesday night, told CNN that she joked about death.
"She said, 'You know I'm 81 years old, and I could drop dead at any moment and you would be so lucky because you will have a story to tell your friends for the rest of your life,' " Lucas said. "Then she mimicked people talking about what it was like to see her drop dead on stage."
CNN's Jennifer Bixler, Carolyn Sung and Doug Ganley contributed to this report.