"I'm deeply sorry for the hurt and embarrassment I've caused to those close to me and everyone this has affected," Stewart said in a statement to People Magazine. "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."
US Weekly broke the story on July 24 after photographers snapped the 22-year-old actress in a series of steamy photos with Rupert Sanders, 41, her director from "Snow White and the Huntsman" in Los Angeles.
Stewart and Pattinson, 26, started dating after working on the "Twilight" films, the last of which is set to be released in November.
Sanders is married to British Vogue model Liberty Ross, and the couple have two children together.
"I am utterly distraught about the pain I have caused my family," Sanders said in a statement to People. "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."