Rivers, 81, was hospitalized in New York after she stopped breathing during outpatient surgery on her vocal cords at a Manhattan clinic.
"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," Melissa Rivers said in a statement. She added that her mother would be overwhelmed by the kindness people have shown and thanked everyone for praying for her mother.
Rivers, an actress and stand-up comedian known for her acerbic brand of humor, has been at Mount Sinai Hospital in Manhattan since Thursday. Life support is provided to a patient to keep vital organs such as the brain, heart, lungs, liver and kidneys working. It can involve medications or devices to keep the heart pumping or a ventilator to help with breathing.
"Most often when a doctor puts a patient on life support, I would imagine that means they are on a ventilator and possibly some other combination for the support for the heart and the kidneys," Dr. Steven Simpson, a critical care specialist at the University of Kansas Hospital in Kansas City, said in an interview.
Although Rivers is 81, he added that age is not as important as the care given immediately after cardiac arrest. "What makes much more of a difference is the duration of the arrest and the success or failure of the initial resuscitation," he said. "Statistically age just doesn't weigh as heavily as you might think."
A doctor will gradually wean a patient off life support as the condition improves.
Rivers, who once described herself as the "plastic surgery poster girl" and joked about her numerous procedures, stopped breathing after suffering cardiac arrest.
A representative for the comedian said media reports that her family was planning to sue the endoscopy clinic where she was treated were not true. During her lengthy career, the husky-voiced, Brooklyn-born comedian won fame for her put-downs and was known for asking, "Can we talk?"
Rivers wanted to be an actress but got into comedy after writing sketches for television's "The Ed Sullivan Show." A career in stand-up followed. She later worked as a regular guest host for Johnny Carson on NBC's "The Tonight Show."
When she started her own late-night talk show in 1986, on the rival Fox network, it caused a falling-out with Carson that lasted until he died in 2005. Rivers' show was canceled after seven months. Rivers also had an Emmy Award-winning daytime talk show, "The Joan Rivers Show," and later hosted "Fashion Police," commenting on the unfortunate red carpet choices of celebrities.
Rivers won Donald Trump's reality TV show "The Apprentice" in 2009 and starred in the reality TV program "Joan & Melissa: Joan Knows Best?"