Comedian Joan Rivers, five days after a near-fatal heart and lung failure, remained on life support Tuesday as her daughter, Melissa, stood vigil at her mom’s bedside. 
 
 Melissa Rivers issued a three-sentence statement that shed little new light on the situation — including the medical options going forward as the “Fashion Police�? host battles to stay alive. 
 
 Rivers went into cardiac and respiratory arrest during a doctor’s visit on Thursday, and medical machines have been keeping her alive since the weekend. 
 
 “On behalf of my mother and our family, we are extremely grateful for all the love and support we have received,�? Melissa Rivers said. 
 
 Rivers' assistant Graham Reed was seen getting into a taxicab Tuesday morning. (Marcus Santos/Daily News) Rivers was hospitalized at Mount Sinai Hospital on Thursday. (Richard Harbus/(Richard Harbus/for New York Dai) 
 
 “At this time, she does remain on life support. 
 
 “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.�? 
 
 Rivers, 81, remained surrounded by family and friends in her room at Mount Sinai Hospital. Her grim-faced assistant, Graham Reed, left the hospital Tuesday morning without comment. 
 
 Several sources told the Daily News that if Rivers pulls through, she’s in for a rehab process that could take months or even years and would keep her out of the public eye. 
 
 A woman whose brother is hospitalized on the same floor as Joan Rivers said Melissa has gone out of her way to treat them nicely despite her own burden. 
 
 “It really affects her, what she’s going through,�? said the woman, who declined to give her name. “She’s hurting, and yet she took the time to really care for us — and she doesn’t even know us.�? 
 
 Joan Rivers (r.) with daughter Melissa Rivers, who has been by her mother’s side since she was hospitalized Thursday. (Astrid Stawiarz/Getty Images) Joan Rivers (l.) with daughter Melissa Rivers, who has been by her mother’s side since she was hospitalized Thursday. ( ERIC THAYER /REUTERS) 
 
 Doctors at Mount Sinai had initially placed Rivers into a medically induced coma as they began running tests on her. 
 
 The medical team hopes to get a read on any damage caused when Rivers stopped breathing last week at an Upper East Side clinic. Rivers was getting her throat checked out. 
 
 bpaddock@nydailynews.com ||||| Comedienne Joan Rivers remains on life support in a New York City hospital, her daughter, Melissa Rivers, said on her mother's Facebook page on Tuesday. 
 
 Rivers, 81, was taken to Mt. Sinai Hospital on Thursday after going into cardiac arrest during a routine procedure at Yorkville Endoscopy on the Upper East Side. Melissa and Rivers' grandson Cooper flew to New York later that same day. 
 
 Earlier Tuesday there were various disputed reports that Rivers was being brought out of her medically induced coma in order to assess possible brain damage. 
 
 Meanwhile there have been conflicting accounts as to the severity of her condition. Just yesterday, a source told the E! Network the comedy queen was "getting better." 
 
 "It's a slow process, but she's on the road to recovery..." a source close to the situation told E!. "Don't believe all this ridiculous speculation," the person added. 
 
 The New York Daily News reported that a taping of Rivers' show, Fashion Police which was supposed to coincide with New York Fashion Week has been cancelled. 
 
 Twitter continues to light up with support from fans of the legendary funny lady. 
 
 
 
 .@Joan_Rivers Get well soon Joan - keep fighting! — Donald J. Trump (@realDonaldTrump) August 30, 2014 
 
 We have a gig in 2 weeks and I'm not doing it without you YOU'RE BEING RIDICULOUS @Joan_Rivers — Sarah Silverman (@SarahKSilverman) August 31, 2014 
 
 4 the first time in years I got down on my knees & prayed tonight! I encourage U 2 do the same 4 @Joan_Rivers my grandma! #inconsolable — Kelly Osbourne (@KellyOsbourne) August 30, 2014 
 
 Sending love, love and more love to Joan. @Joan_Rivers — Jane Lynch (@janemarielynch) September 1, 2014 
 
 Dear @Joan_Rivers, FYI the flowers u JUST sent me r still goin strong! Thinking of U every minute. LUV U #JoanRivers pic.twitter.com/VWXe0Xb85e — Kathy Griffin (@kathygriffin) September 1, 2014 
 
 Oh, Joanie. This isn't funny. Please wake up. I promise I'll be your piano player...for free again! Loving you and praying for @Joan_Rivers — Barry Manilow (@barrymanilow) September 1, 2014 
 
 Please keep praying for Joan. RT @nikkibrooks88: @Joan_Rivers @MelRivers wishing the wonderful, clever, funny Joan a full & speedy recovery — Giuliana Rancic (@GiulianaRancic) August 31, 2014 
 
 It's Sunday morning and I am praying for a miracle for the great Joan Rivers. The world needs Joan. 🙏🙏 — Andy Cohen (@Andy) August 31, 2014 
 
 We can't lose Joan. All love and healing wishes to Her Majesty Joan Rivers- being ripped a new one by you is an honor to be treasured. — Lena Dunham (@lenadunham) August 31, 2014 
 
 Sending love to my pal, Joan Rivers. — Joy Behar (@JoyVBehar) August 29, 2014 
 
 I’m thinking about you, @Joan_Rivers, and sending lots of love your way. — Ellen DeGeneres (@TheEllenShow) August 28, 2014 ||||| Christopher Polk/Getty Images 
 
 Joan Rivers is a fighter. 
 
 As the E! Fashion Police host remains hospitalized at Mount Sinai Hospital in New York City, a source reveals the comedian is making small, but positive, steps. 
 
 "It's a slow process, but she's on the road to recovery," a source close to the situation tells E! News exclusively. "She's getting better. Don't believe all this ridiculous speculation." 
 
 Joan stopped breathing while undergoing a minor throat procedure Aug. 28 in New York City. She was then rushed to the hospital where she was placed in a medically induced coma. 
 
 Her daughter, Melissa Rivers, flew across the country the same day with her son, Cooper, to be by the comic legend's side. 
 
 NEWS: Fashion Police co-hosts send heartfelt prayers to Joan Rivers 
 
 "She is a rock. She is calmer than I've ever seen her," the source told E! News in 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." 
 
 The insider added, "She's focused on one thing: Her mother's health." 
 
 Joan remains in stable, yet critical, condition. On Sunday, Melissa thanked fans for all their prayers and well wishes. 
 
 "Thank you for your continued love and support," she said in a statement. "We are keeping our fingers crossed." 
 
 Our thoughts and prayers continue to go out to the Rivers family at this time. 
 
 PHOTOS: Check out the best jokes Joan Rivers has made about celebs 
 
 RELATED VIDEOS: ||||| University of Denver Official Facebook Page 
 
 The official Facebook page of the University of Denver in Denver, Colorado.
– Joan Rivers is still on life support, her daughter says on Facebook, per the Wire. "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," Melissa Rivers notes. Family and friends are with Rivers in the hospital, the New York Daily News reports. Yesterday, a source to E! News said Rivers was "on the road to recovery," though slowly, while other reports said she was being brought out of a medically induced coma. A recovery would be followed by a months- or years-long rehab period during which she wouldn't appear publicly, insiders tell the Daily News.