People reported about the fling and quoted a source saying Stewart and Rupert Sanders were not having an affair and that "it was just a fleeting moment that shouldn't have happened."
The source added that Stewart "never meant to hurt anyone. She's a good person who just made a bad choice."
Stewart herself has now released a statement to People about the incident saying, "I'm deeply sorry for the hurt and embarrassment I've caused to those close to me and everyone this has affected. This momentary indiscretion has jeopardized the most important thing in my life, the person I love and respect the most, Rob. I love him, I love him, I'm so sorry."
The 41-year-old Sanders, who is 19 years older than Stewart, is married to actress/model Liberty Ross and they have two young children. Ross appeared as a young Stewart's mother in Huntsman.
Sanders issued his own apology to People saying, ""I am utterly distraught about the pain I have caused my family."
"My beautiful wife and heavenly children are all I have in this world. I love them with all my heart. I am praying that we can get through this together," he added.
Stewart and Pattinson met while filiming the first installment of Twilight and rumors about them being an off-screen couple began almost immediately.
The pair denied being in a relationship at first but have become increasingly open about it recently.