Britain's most successful gymnast Beth Tweddle has walked "a few steps" with assistance from medics following neck surgery - but a timescale for her recovery is uncertain, her parents said.
The 30-year-old, who won bronze at the London Games in 2012, fell on the slopes during rehearsals for Channel 4 celebrity show The Jump and needed neck surgery which involved having a piece of bone taken from her hip.
In a statement, Tweddle's parents Ann and Jerry said: "Since her surgery, Beth has managed to walk a few steps whilst being assisted by the nursing team.
"She is still very tired from the operation but the medical team are pleased with the progress she is making. At the moment we aren't certain of the timescale for her recovery. We are taking each day as it comes and will update you when there is further news."
The operation saw surgeons take a bone from her hip and use it along with pins to fuse together two fractured vertebrae in her neck.
Tweddle's parents added: "The medical staff here in Austria have been fantastic, they have been so helpful, patient and incredibly attentive. We cannot thank them enough for what they've done for our daughter.
"Our thanks also go to the production team who have been helping and supporting us, and everyone who has sent a get well message to Beth.
"We've been reading every message to her and it really does make a difference knowing that there are so many people wishing her well. Thank you for your support."
Speaking from her hospital bed on Monday after the surgery, Tweddle described the previous 48 hours as "very scary".
The number of injuries on the third series of The Jump - four celebrities have been forced to pull out - has prompted Channel 4 to confirm that it will review safety procedures on the show.
The broadcaster said this year's events have been designed to be "no more difficult than in previous years" and said all celebrities have undertaken a rigorous training programme to prepare them for the show.
A statement added: "All winter sports carry some element of risk but in light of the number of injuries this year, Channel 4 has asked the producers to review safety procedures again to further reduce the prospect of accident."
Olympian Rebecca Adlington, 26, withdrew from the show on medical advice after a shoulder injury.
She told host Davina McCall the pain of the fall was ''literally the worst thing that has ever happened to me, it was worse than childbirth''.
Holby City actress Tina Hobley, 44, also headed for the exit after she dislocated her elbow and suffered two fractures to her arm.
On Tuesday it was confirmed that Made In Chelsea star Mark-Francis Vandelli, 26, had also pulled out after fracturing his ankle.
Although he has not ruled himself out of the show, the future looks uncertain for former athlete Linford Christie, 55, who was unable to take part in an event on Sunday after pulling his hamstring.
And former EastEnders star Sid Owen, 44, was unable to perform the air jump live due to injury.
British former ski jumper Eddie ''The Eagle'' Edwards defended the show's producers and said that celebrities should ''bear the brunt of the blame'' for any injuries they suffer while taking part in the show.
The 52-year-old, who represented Britain at the 1988 Winter Olympics and worked as an expert on the previous two series of The Jump, said the growing number of stars on the injury list was not ''solely'' down to producers and suggested the contestants needed to practise more.