"I want to thank everyone for the overwhelming love and support for my mother," Melissa said in a statement. "She is resting comfortably and is with our family. We ask that you continue to keep her in your thoughts and prayers."
The Fashion Police star, 81, was rushed to Mount Sinai Hospital on Thursday after complications occurred during a throat procedure on her vocal cords. She has reportedly been placed in a medically induced coma after being upgraded from critical to stable condition.
Meanwhile, those who saw the actress just a day ago say they are "shocked" by the news.
"Joan was energetic and boisterous," a source tells PEOPLE about the star's appearance at an event promoting her new book, Diary of a Mad Diva. "She looked amazing [and] was high-energy."
Like her usual sharp-tongued self, Rivers "had everyone laughing, and it didn't stop for an hour," the source adds.
With reporting by EMILY STROHM and JANINE RAYFORD RUBENSTEIN