Police are investigating the incident on Sunday at Tate Modern gallery on the River Thames, where witnesses saw a man approach Rothko's 1958 canvas "Black on Maroon" and inscribe it with black ink in the lower right-hand corner.
Although the ink had run down the canvas, a photograph posted by a witness on the Twitter website showed the words: "VLADIMIR UMANETS '12, A POTENTIAL PIECE OF YELLOWISM."
A man answering a mobile phone number provided via a link on the website of the "Yellowism" movement (www.thisisyellowism.com) answered to the name of Vladimir Umanets and told Reuters he had carried out the attack.
"I'm aware they (the police) will come at some point and arrest me," he said, speaking in an eastern European accent.
"It was an artistic statement, but it was more about having the opportunity to speak about galleries and art," he added, explaining his actions.
"Marcel Duchamp, when he made 'readymades' (art), everyone was shocked. I don't want to be considered a vandal or someone who wants to destroy something, especially such a valuable painting.
"It's more about to change perception of things, of spectators. It's more about an idea."
Duchamp's iconoclastic urinal, entitled "Fountain" and featuring the words "R.Mutt", is considered one of the most influential works of the 20th century by challenging people's understanding of what constitutes art.
"What I do believe is the most creative thing left to do in contemporary art today is to abandon this (art) and Marcel Duchamp was trying to do this," Umanets said.
"I'm not saying I'm another Marcel Duchamp. I'm not a tag-maker. I'm doing my own thing ... After Duchamp, nothing actually happened. I definitely believe that Marcel Duchamp would be really happy."
In its online manifesto, "Yellowism" is described as neither art nor anti-art and that the "context for works of art is already art".
The Metropolitan Police said the suspect was a white man believed to be in his late-20s. No arrest has been made.
A Tate Modern spokeswoman said the painting would be repaired by an in-house team of experts. Asked whether the gallery, one of the world's most popular, was considering beefing up its security, she replied in a statement:
"Tate has strong security systems in place including physical barriers, security officers in the galleries, alarms and CCTV."
In the case of the Rothkos, which are hanging on Level 3 of the converted power station, the barrier is a low wire.
The damaged work was one of the "Seagram Murals" the Russian-American artist was commissioned to paint in the 1950s for the new Four Seasons restaurant in New York.
Several ended up in the Tate collection after they were given as gifts before Rothko took his life, and Tate describes the famous series of soft-edged rectangles as "iconic".
No one knows why the artist abandoned the bright, intense colors of his earlier canvases and painted in dark maroons, reds and black, but one theory is that he said he wanted to "ruin the appetite of every son of a bitch who ever eats in that room."
Rothko is considered one of the 20th century's most important artists, and in May, his "Orange, Red, Yellow" sold for $86.9 million, a new auction record for the artist, at Christie's in New York.
Tim Wright, who witnessed Sunday's attack, wrote on Twitter: "This guy calmly walked up, took out a marker pen and tagged it. Surreal ... Very bizarre, he sat there for a while then just went for it and made a quick exit."
(Reporting by Mike Collett-White)
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