Mr Graham, 80, of Newcastle upon Tyne, admitted putting up the marble monument in the field where Hess is thought to have landed on his flight to Britain in 1941.
He condemned anti-Nazi activists who demolished the monument earlier this week, as 'Communist gangsters', and claimed Hess was 'a great man who sought peace'. He said he was heartened that it had become a shrine for neo-Nazis.
Mr Graham said: 'Hess was the only man to stick up for the white race, for ordinary decent people. He would have prevented us being overrun by outsiders.' He dismissed as 'lies' evidence that the Nazis murdered 6 million Jews.
In Germany, Michael Swierczek, leader of the banned neo-Nazi group Nationale Offensive, said: 'It would be a mistake to imagine that those who put the memorial up in the first place are now going to give up just because the Anti- Nazi League pulled it down. There will certainly be an attempt to put up a new memorial . . . If you Britons can put up statues to Arthur 'Bomber' Harris, then why should there not be one to Hess?'
He added: 'On the far right in Germany, we have known about this for many months. Many of the older members of the scene have been to see it and come back to tell us about it and show us photos.'
Mr Graham confirmed that in November last year he approached Craig Baird, the owner of Floors Farm, near Glasgow, for permission to erect the stone. He returned in May to carry out the work.
Mr Graham's involvement in extreme right politics is well documented. He has attended meetings of the British National Party in Sunderland, and - according to Searchlight, the magazine which monitors the far right - has been on marches in Germany and Belgium commemorating Hess's death six years ago.
Hess's flight in May 1941 remains one of the most bizarre episodes of the Second World War. He was believed to have been carrying proposals for peace between Britain and Germany but he was arrested and later jailed for life at the Nuremberg war crimes trial.
Lord James Douglas-Hamilton - son of the Duke of Hamilton, the Scottish landowner to whom Hess wanted to present his plans - said: 'Hess's proposals consisted of a limited peace under which Germany would have allowed Britain a free hand in her empire in return for Britain allowing Germany a free hand in Europe and Russia. His so- called peace plans would have meant the enslavement of Europe.'
Lord James, author of The Truth about Rudolf Hess, said: 'Hess was an architect of the Nazi machinery and shared Hitler's thinking to the last. The monument was totally inappropriate.'
At Floors Farm yesterday, Mr Baird said he had destroyed the remains of the memorial and abandoned plans to erect a replacement.