Joan Rivers is still on life support after complications from throat surgery last week, her daughter confirmed.

The 81-year-old comedian went into cardiac arrest while undergoing a minor vocal cord procedure at a clinic in New York City on Thursday. She briefly stopped breathing and was immediately taken to Mount Sinai Hospital, where she was pronounced in stable but critical condition.

Her daughter, Melissa Rivers, released a statement to media outlets on Tuesday afternoon that gave an update on her status and thanked fans for their kind words.

“On behalf of my mother and our family, we are extremely grateful for all the love and support we’ve received. At this time she does remain on life support,” she said. “I know my mother would be overwhelmed by the continued outpouring of kindness and I want to thank everyone for keeping us in their prayers.”

Since Rivers has been in the hospital, reports have been flying back and forth about her status. Earlier Tuesday, E!, which airs Rivers’s “Fashion Police,” quoted a source as saying Rivers was “getting better,” adding, “It’s a slow process, but she’s on the road to recovery.”

In addition to “Fashion Police,” Rivers has a Web series called “In Bed With Joan” that she hosts with Melissa Rivers. She was also scheduled to perform several weeks of shows in Europe this fall, on a tour called “Quick…Before They Close the Lid (Seriously…this one could be IT!).”

Many celebrities spoke out wishing Rivers well last week and through the weekend: