Joan Rivers -- Still in Serious Condition

Joan Rivers remains in serious condition but is receiving the best treatment possible ... so says her daughter, Melissa Rivers.

Melissa just released a statement thanking everyone for their support ... adding that Joan would be touched.

TMZ broke the story ... Joan was rushed to Mount Sinai hospital in NYC Thursday morning after she stopped breathing during a procedure on her vocal cords.

After originally being listed in critical condition ... she's been "resting comfortably" and surrounded by family since late Thursday afternoon, according to her daughter.