The longtime couple are the stars of the romantic "Twilight" vampire film franchise and have been dating for several years.
Several media outlets reported Tuesday Stewart, 22, recently had a brief fling with director Rupert Sanders, who is 41, married and the father of two children.
TMZ said Stewart publicly confirmed the affair Wednesday and apologized to Pattinson, 26.
"I'm deeply sorry for the hurt and embarrassment I've caused to those close to me and everyone this has affected," the actress said. "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."
Sanders issued a separate statement to People.com Wednesday.
"I am utterly distraught about the pain I have caused my family," said Sanders, who is married to actress-model Liberty Ross. "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."