The man, who identified himself as Vladimir Umanets, scrawled "Vladimir Umanets, A Potential Piece of Yellowism" across the canvas of the late Mark Rothko's "Black on Maroon" Sunday afternoon and then fled the gallery, The Daily Telegraph reported.
Umanets, who is originally from Russia, said on his website the "Yellowism" movement is "an autonomous phenomenon in contemporary culture."
He told the BBC Monday he is not a vandal and is a fan of Rothko.
"I haven't done criminal damage. Art allows us to take what someone's done and put a new message on it," he told the British network.
"There will never be another Rothko in the world ever. I would like to show such a wonderful piece in the context of yellowism."
Efforts were under way to determine if the 1958 painting could be fully restored.
Rothko died in 1970. His children, Kate Rothko Prizel and Christopher Rothko, said in a statement the family is "greatly troubled" by the attack on their father's painting, but is "heartened" by the public support expressed since it happened.