British eventer William Fox-Pitt has been called a "fantastic ambassador" as equestrian followers wish him well following a head injury.
The former world number one is under sedation in a French hospital after a fall on the cross-country course at the World Young Horse Championships.
Fox-Pitt, 46, was thrown to the ground when his uninjured horse hit a fence.
"There has been a tremendous amount of support from everyone," said Team GB equestrian chief Yogi Breisner.
Father-of-four Fox-Pitt, who is married to Channel 4 racing presenter Alice Plunkett, is GB's most successful rider with 20 major championship medals.
On Tuesday night, Plunkett tweeted that her husband "remains stable and under sedation. He is in great hands and is progressing well. Thank you again for all your support".
Fox-Pitt's achievements include three Olympic team podium finishes and six European team gold medals for Great Britain. He won this year's Badminton Horse Trials on his horse Chilli Morning.
"William has been on just about every British team for the last 20 years. He has been a fantastic ambassador," Breisner told BBC Sport.
"He has been number one in the world, had more four-star rides than any other rider, and has won individual medals at World and European Championships."
Fox-Pitt, who is based at Sturminster Newton in Dorset, was competing on Reinstated in the seven-year-old class at Le Lion-d'Angers.
"He is is being monitored but the hospital haven't given any timings whatsoever," said Breisner.
"They just don't know and it will depend on how the brain reacts and when they bring him out of sedation."
Fox-Pitt is not thought to have any other significant injuries and the sedation is a way of protecting the brain from swelling.
"There has been a tremendous amount of support from everyone. Our thoughts are with William and his family. He is in one of the leading hospitals in France and is being taken care of by specialists," added Breisner.