Show jumper Jonty Evans has regained consciousness and "is beginning to interact positively with the medical team and his family".
Evans suffered a fall during the Tattersalls International Horse Trials in June.
A statement from his family read: "We are pleased to report that over the past 10 days Jonty's condition has continued to slowly improve. Jonty has now regained consciousness and is beginning to interact positively with the medical team and his family.
"Jonty is having physiotherapy and rehabilitation sessions, which will continue for the foreseeable future as he regains strength and his head injury continues to improve.
"Due to the need for Jonty to remain in a quiet and calm environment for a significant period of time, and to continue his recovery as privately as possible, the medical team have advised the family to keep visitors strictly to a minimum.
"The family deeply appreciate all the actions, support and kind words that Jonty has received over the past weeks from the Eventing Community - they have found this a great source of strength.
"If you wish to make a donation, the family’s chosen charity is the David Foster Injured Riders Fund http://www.davidfosterinjuredridersfund.ie/
"Jonty’s family thank everybody for their kind thoughts, continued support and best wishes."
Horse Sport Ireland had already confirmed that the 46-year-old suffered a "significant brain injury" after falling from Cooley Rorkes Drift during the cross-country phase of the CIC three-star competition in Co Meath on 3 June.
