Burton claimed Affleck, 45, groped her when she was a host of MTV's TRL in 2003.
"I acted inappropriately toward Ms Burton and I sincerely apologise," Affleck tweeted.
The incident on TRL resurfaced after Affleck condemned the sexual harassment allegations against Harvey Weinstein saying he was "saddened and angered" by claims of alleged sexual harassment and assault made against the movie mogul by some of the biggest celebrities in Hollywood.
After a fan suggested that Affleck should have "kept quiet," another Twitter user wrote, "He also grabbed Hilarie Burton's breasts on TRL once. Everyone forgot though."
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The "One Tree Hill alum" then shared a clip of TRL outtakes in which she says, "He comes over and tweaks my left b**b," apparently speaking about Affleck. Later in the video, the actor is shown asking her, "How old are you 19?"
"Girls. I'm so impressed with you brave ones," Burton, who is expecting her second child with "The Walking Dead" star Jeffrey Dean Morgan, wrote in the tweet. "I had to laugh back then so I wouldn't cry. Sending love."
Social media users also compared the incident with another interview of Affleck conducted in 2004 by Montreal TV host Anne-Marie Losique.
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