Elliott made a public apology last night for any offence caused by a photograph that emerged on social media.
Gigginstown House Stud owner Michael O'Leary has said he will "continue to support" trainer Gordon Elliott.
Elliott made a public apology last night for any offence caused by a photograph that emerged on social media of him sitting on a dead horse.
O'Leary - who enjoyed Cheltenham Gold Cup and Grand National success with the Meath trainer - said in a statement today that the "care and welfare of all our animals comes first".
But he adds that he believes it was a "momentary lapse of judgement" and that he accepts the apology.
The Irish Horseracing Regulatory Board launched an investigation into the photo yesterday.
Elliott says that he is cooperating fully with the IHRB.
The trainer says the image was taken some time ago, and came after the sudden death of one of his horses on the gallops.

In the picture, Elliott appears to be making the "peace" gesture with his fingers.
However in his statement, he claims he was gesturing to a colleague to wait until he was finished with his phonecall.
Horse Racing Ireland say they unreservedly condemn the "disturbing" photograph.
H-R-I also say they are supporting the I-H-R-B investigation into the picture.
While the British Horseracing Authority is considering its own regulatory options.
In a statement the B-H-A say it is appalled by the image and that people who work in the industry have been "deeply undermined" by this behaviour.
— Gordon Elliott (@gelliott_racing) February 28, 2021
Westmeath SHC: Ending Championship Drought On The Cards For Lough Lene Gaels
Midlands LGFA Champions Looking To Book Provincial Semi-Final Spots
Laois SFC: Consistency The Message From Portarlington Manager
Portlaoise Panthers Aiming To Return To Winning Ways
Westmeath SHC: Castletown Geoghegan And Lough Lene Gaels Set For Bank Holiday Clash
Buccaneers Travel To Wexford In AIL This Weekend
Offaly SFC: Ferbane Looking To End Six Year Championship Drought
Laois SFC: A Second Chance Awaits Courtwood
Portlaoise Panthers Looking To Continue 100% Start
Westmeath SFC: Coralstown Kinnegad Looking To End 29 Year Famine
Offaly SFC: Tullamore And Ferbane Set For Trilogy
Milltown Secure Westmeath Ladies Football Championship
Medals Secured For Midlands Boxer At European U15 Championships
Westmeath SFC: A Repeat Of 2022 The Motivation For The Down's
Westmeath Seeks Government Backing For €78m Sports Complex Plans
Offaly SHC: Shinrone Fightback Not Enough In The End
Clara Star Nominated For Player Of The Year Award
"There's Work To Be Done To Sign Players"
CCFL: Scoreless Draw Leaves Clonaslee Bottom Of Senior Division
Laois SHC: Champions Stand Up To Be Counted When It Matters Most