Rivers' doctors were intentionally keeping her sedated and under close supervision at Mt. Sinai Hospital in New York City until they were more comfortable with the 81-year-old's condition, the source said.
Rivers' daughter, Melissa Rivers, said in a written statement today that her mother's condition remained serious.
"My mother would be so touched by the tributes and prayers that we have received from around the world. Her condition remains serious but she is receiving the best treatment and care possible," Melissa Rivers said. "We ask that you continue to keep her in your thoughts as we pray for her recovery."
Melissa Rivers arrived at the hospital around 8 p.m. Thursday night and has been joined by Rivers' personal assistant, publicist and reps from E!, the network that airs her show, "Fashion Police," the source familiar with the situation said.
On Thursday morning, Rivers was rushed to Mount Sinai Hospital in New York City after an emergency call that she was in cardiac arrest at an Upper East Side clinic, Yorkville Endoscopy, sources said. TMZ reported that Rivers was undergoing a procedure on her vocal chords at the clinic.