Psy issued a statement after US media reported he had performed in concerts protesting against the American presence in South Korea and Iraq.
The singer said he would “forever be sorry” for any pain he had caused.
Psy is due to perform at the annual Christmas in Washington TV special.
President Barack Obama and his family are expected to attend the concert.
Psy’s hit song Gangnam Style is the most-watched video ever on YouTube, with more than 900 million views since it was uploaded in July.
However, at a concert in 2002 protesting against the US military presence in South Korea, Psy smashed a model of a US tank on stage.
At another concert in 2004, Psy performed a song that described killing “Yankees” who had tortured Iraqi prisoners and killing their families “slowly and painfully”.
The lyrics were from the song Dear American by South Korean metal band Next.
“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,” Psy wrote in the statement.
“I will forever be sorry for any pain I have caused by those words.”
Psy, who attended college in the US, said he understood “the sacrifices American servicemen and women have made to protect freedom and democracy in my country and around the world”.
He added: “I have been honored to perform in front of American soldiers in recent months… and I hope they and all Americans can accept my apology.”
The singer’s participation in the protests was no secret in South Korea but unknown in the US until recently, AP news agency reported.
The White House has confirmed that President Barack Obama and his family will attend the charity concert on December 21st at which Psy will perform.
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