Stewart was reported over the last few days to have embarked on a "brief fling" with her married Snow White and the Huntsman director Rupert Sanders.
Photos seemingly showing the pair together were published in US magazines, but the reports had yet to be confirmed.
Stewart has now released a statement owning up to the betrayal, in which she apologises profusely for "the hurt and embarrassment" caused by her "momentary indiscretion".
She said: "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 jeopardised 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."
Photo gallery - Kristen Stewart and Robert Pattinson's relationship so far:
Copyright: WENN> Rupert Sanders on Kristen Stewart fling: 'I'm utterly distraught'
The status of Stewart's relationship with Pattinson and Sanders's marriage is not yet known, though the filmmaker's wife Liberty Ross tweeted a message when the news of the affair broke, reading: "Sometimes good things fall apart so better things can fall together."
Stewart and Pattinson met when filming the first Twilight movie in 2008.
Watch a trailer for Kristen Stewart and Robert Pattinson's The Twilight Saga: Breaking Dawn - Part 2 below: