Joan Rivers's daughter Melissa Rivers issued a statement about the legendary comedienne's condition today. The younger Rivers said, "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. 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."

Rivers, 81, has been in a medically-induced coma at Mount Sinai Hospital since Thursday night, hours after going into cardiac arrest during an endoscopic procedure at a Manhattan clinic. A source told E! that Rivers is making some progress, "It's a slow process, but she's on the road to recovery. She's getting better. Don't believe all this ridiculous speculation."

The source also said of Melissa Rivers, "She is a rock. She is calmer than I've ever seen her. All these reports about doomsday are not true. She is her mother's daughter and she's tough as nails. She's the person keeping everyone together."

A Daily News source said that the family was going to start the process of trying to take Rivers out of the coma and that they were considering suing the clinic where Rivers was getting the endoscopy.