Joan Rivers remains in a serious condition in a New York City hospital, one day after going into cardiac arrest at a doctor's office.
Melissa Rivers said that her mother was "receiving the best treatment and care possible". She also thanked Rivers' fans and friends for their support.
"My mother would be so touched by the tributes and prayers that we have received from around the world," Melissa said. "Her condition remains serious ... We ask that you continue to keep her in your thoughts as we pray for her recovery."
The comedian with a half-century of showbusiness under her belt has spawned a reputation for often-snarky red carpet fashion commentary. A show she had scheduled for today at the Count Basie Theatre in New Jersey has been postponed.
An early and outspoken proponent of cosmetic surgery, Rivers drastically altered her appearance over the years - and found plenty of material for jokes. "I've had so much plastic surgery, when I die they will donate my body to Tupperware," she said.
The host of Fashion Police on E! network, Rivers also presides over an online talk show, In Bed With Joan, and co-stars with her daughter on the WEtv reality show, Joan & Melissa: Joan Knows Best?"
Stars have been sending their best wishes to the Fashion Police star on Twitter.
Heroes star Zachary Quinto tweeted: "sending so much love and healing energy to @Joan_Rivers !!! no one is ready to go on without you lady!!!"
Modern Family actor Jesse Tyler Ferguson wrote: "Sending all my love and prayers to my friend @Joan_Rivers right now."
Actress Marlee Matlin tweeted: "Get well @Joan_Rivers! And moon the doctors for us while you're recuperating!"
American TV host Billy Bush wrote on his Facebook page that Melissa Rivers had told him to "please pray".
He wrote: "Praying for Joan Rivers who is in critical condition at Mt Sinai hospital in NY. Texted with Melissa Rivers who said "please pray". Already doing that. Joan is beloved around here.
"A regular guest on Access Hollywood Live she never fails to deliver. She taped her post Emmy special Tuesday in LA and was strong. This is out of nowhere. Come on Joan you have to make it. Just think of all the material. Sending love and prayers."
Actress Kelly Ripa tweeted: "Praying for the great @Joan_Rivers one of the true loves of my life."
And Courtney Love Cobain told her 344,000 followers: "Hang in there @Joan_Rivers So many awful gowns are going to be worn this year as bait for you pull through. Love and prayers Court."