Updated August 31 at 5:51 p.m. ET
"We are keeping our fingers crossed," Melissa Rivers, said in a statement released to the Associated Press, thanking people who have expressed support for the 81-year-old comedian.
"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 is now spending her fourth day on life support in a NYC hospital after being admitted on Thursday.
The legendary comedienne is still completely reliant on machines to stay alive, and her family is struggling to cope with this news, especially Joan's daughter Melissa.
Joan was undergoing throat surgery Thursday at a clinic, reportedly on her vocal chords, when she stopped breathing. She was quickly rushed to NYC's Mount Sinai hospital, where she remains.
Melissa arrived that same day to visit her mother, and now it seems that she may be tasked with making that one decision no one wants to make.
To make matters worse, Melissa is having a very difficult time as her mother's condition continues to stay the same.
“She still thinks everything is going to be OK. She is refusing to admit that a world might exist without her mother in it,” said a source close to the Rivers family told the Daily News.
"Others that are close to Joan are starting to realize that the outcome they want is very unlikely".”
Sources who spoke to TMZ claim that the family will have to decide in the next couple of days whether to keep the 81-year-old on life support.
Some family members believe if they take her off, her condition will improve and she will fight through and win this battle.
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