The 81-year-old comedian was rushed to Mount Sinai Hospital in New York City on Aug. 28. Rivers was undergoing an outpatient procedure on her throat at Yorkville Endoscopy in Upper Manhattan when she went into cardiac arrest.
On Wednesday, Rivers' daughter Melissa issued a statement that her mother had been moved out of intensive care and into a private room where she is being "kept comfortable."
Doctor's office is under investigation.
The New York state health department is investigating Yorkville Endoscopy, the clinic where Joan Rivers was undergoing a routine procedure when she went into cardiac arrest last week.
The New York State Health Department told ABC News that it has opened a "full investigation," into the clinic.
Melissa Rivers issued another brief statement, this time saying her mother has been moved out of intensive care.
Melissa Rivers gave a brief statement to the New York Times in which she says her mother is still on life support.
Entertainment Tonight is reporting that doctors have begun the process of bringing Rivers out of the medically induced coma.
The New York Daily News reports the process will take until Tuesday, when doctors can then assess the extent of any damage Rivers may have sustained during her cardiac and respiratory arrest:
"The waking-up process has begun and will take until Tuesday," a source close to the family told the Daily News. "There is real concern that the part of the brain that controls motor skills may have been compromised, leaving her as either a vegetable or in a wheelchair."
There were no significant changes to Rivers' condition on Sunday.
The Rivers family is "keeping our fingers crossed," NBC News reported. The comedy legend is still on life support in the hospital, Melissa Rivers told NBC.
Joan Rivers has been put on life support, TMZ reported.
One source told TMZ that in the next few days the family will be deciding whether to keep Rivers on life support.
"We're told the family remains hopeful that if they do decide to turn off the machines, she will make a turn for the better and fight through it," reported TMZ.
Melissa Rivers issued a statement on her mother's condition:
"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. We ask that you continue to keep her in your thoughts as we pray for her recovery."
Joan Rivers was placed in a medically induced coma Thursday, which she will remain in until the weekend. Doctors will then discuss with Rivers' family the details of damage caused to her when she stopped breathing, the New York Daily News reported.
Melissa Rivers, Joan's daughter, arrived in New York Thursday night, after flying from Los Angeles, and issued a statement that said her mother is "resting comfortably" in the hospital.
"I want to thank everyone for the overwhelming love and support for my mother. She is resting comfortably and is with our family. We ask that you continue to keep her in your thoughts and prayers," she said.
Sid Dinsay, a spokesman for Mount Sinai Hospital, issued a statement about Rivers' admittance to the hospital.
"This morning, Joan Rivers was taken to The Mount Sinai Hospital in New York, where she is being attended to. Her family wants to thank everybody for their outpouring of love and support," Dinsay said. "We will provide an update on her condition as it becomes available."