Vandals have targeted the ancient Uffington White Horse in Oxfordshire by spraying part of it purple.
Officers from Thames Valley Police were called to the 3,000-year-old chalk monument at about 2200 BST on Thursday.
They found the head and eye of the horse had been sprayed with purple paint. A banner that read "fathers 4 justice stop the secret family courts" was recovered from the scene.
New Fathers 4 Justice and Real Fathers for Justice both denied responsibility.
Police and members of the National Trust have been working to re-chalk the monument.
Sgt Steve Clark said: "The monument has been pretty much restored now and is back to how it should look.
"This was a mindless act of criminal damage on an ancient monument and I would urge anyone with information about the incident to come forward and speak to us as soon as possible."
Richard Henderson, the National Trust's general manager for Oxfordshire, said: "We are appalled by this act of mindless vandalism to one of the country's most famous ancient monuments.
"It is particularly sad as only last weekend members of the public helped re-chalk the horse as part of a traditional community volunteering event."
The White Horse at Uffington is the oldest dated chalk figure in the country and forms part of a landscape of ancient sites.
The original group called Fathers 4 Justice was closed down in 2008. A group called the New Fathers 4 Justice formed shortly afterwards.
A spokesman for the New Fathers 4 Justice, calling himself Captain Equality, denied any responsibility for the attack, saying: "Fathers have started using the name for their own protest but we don't condone vandalism, it's not our style."
A rival group calling themselves the Real Fathers for Justice who claim to have been operating since 2005, also distanced themselves from the stunt.
A spokesman said: "They should've picked a legitimate target like a courthouse not an historic monument which should be protected for our children.
"This is criminal damage and nothing's going to be achieved by that."