Joan Rivers Remains on Life Support, Says Daughter Melissa: "We Are Extremely Grateful for All the Love"

"I know my mother would be overwhelmed by the continued outpouring of kindness," Melissa said in a statement

Melissa Rivers has given an update on mother Joan River's health as she continues to fight for her life. 

"On behalf of my mother and our family, we are extremely grateful for all the love and support we've received," Rivers said in a statement, obtained by E! News. "At this time she does remain on life support." 

She added: "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." 

On Thursday, the 81-year-old Fashion Police host stopped breathing while undergoing a minor throat procedure in New York City. She was then rushed to the hospital where she was placed in a medically induced coma.

Her daughter, Melissa, flew across the country the same day with her son, Cooper, to be by the comic legend's side.

In the wake of Rivers' road to recovery, there have been reports speculating that Melissa is considering taking legal action against the endoscopy clinic where Joan was treated, however, a source close to the situation wants to clarify that the rumors "couldn't be further from the truth. Right now, she [Melissa] is 100 percent focused on her mother's health. Any story suggesting otherwise is the stuff of fairies and elves—it's fantasy." 

With regards to Joan's current condition, the source adds that "everyone is hopeful and taking it day by day."

Meanwhile, production on two Fashion Police episodes from New York Fashion Week has been halted as Rivers remains on life support. 

"We will not be producing a Fashion Police this week or next as we await Joan and Melissa's return in front and behind the camera," the network said in a statement today. "E! will be airing two E! From Fashion Week specials that will deliver the latest news and information from the highly-anticipated event."

Earlier this week, a source told E! News that Melissa has been "a rock" following her mother's hospitalization. "She is calmer than I've ever seen her," the source told E! News with regards to Melissa. "All these reports about doomsday are not true. She is her mother's daughter and she's tough as nails. She's the person keeping everyone together."

Our thoughts and prayers go out to the Rivers family during this difficult time. 

—Additional reporting by Ken Baker