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
Three Westmeath Players Named On Intermediate Team Of The Year
Athlone Town Looking To Win Fourth Straight League Game
Aoife O’Brien Takes Rás na mBan Lead
Offaly SHC: Ballinamere Looking To Seal Semi-Final Spot
Athlone Town Continue Push For Women's Premier Division Title
Laois SHC: Five Games To Conclude Group Stages
Katie Taylor Set For Final Fight At Croke Park
Westmeath SFC: Semi-Final Place Up For Grabs
Westmeath SFC: Four Draws Leave St Loman’s Needing Caulry Win
Alex Dunne Returns To Formula Two Action In Monza
Offaly F2 Star Launches Cannonball Charity Partnership
Westmeath SFC: Garrycastle Continue Push For Place In Knockout Stages
Record Time Broken At Tullamore Half Marathon
Offaly SFC: Clara Manager Delighted To Progress To Knockout Stages
Athlone Town Seal Third League Win In A Row
Westmeath SFC: St Loman's And Coralstown Kinnegad Finishes As Draw
Offaly SFC: Ferbane And Rhode Book Semi-Final Spots
Athlone Town Take Big Step Towards Retaining Premier Division Title
Athlone Town Looking To Maintain Lead In Women's Premier Division
Pat Colgan Pedal The Peaks Challenge Set For Sunday