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Psy issued the apology after reports surfaced in the United States on Friday (local time) about his participation in two performances critical of the US military in 2004.
Psy's "Gangnam Style" Korean pop and dance video is now the most-watched video on YouTube, with more than 900 million views since it was first uploaded in July.
"While I'm grateful for the freedom to express one's self, I've learned there are limits to what language is appropriate and I'm deeply sorry for how these lyrics could be interpreted," the rapper said in a statement.
"I will forever be sorry for any pain I have caused by those words," he added.
In one performance, which Psy said was from eight years ago, the rapper protested the deaths of two teenage South Korean girls who were run over by a US tank stationed in the country.
In a separate performance, Psy was critical of the US-led invasion of Iraq and its occupation, in which South Korean forces participated.
Psy is scheduled to perform at the annual "Christmas in Washington" television special which will also be attended by Obama and his family, the White House said. Broadcaster TNT said Psy would still perform as planned.