The 22-year-old actress issued her apology to People Magazine on Wednesday. It was quickly followed by an apology to People from the 41-year-old Sanders to his family. Stewart has been in a relationship for several years with Pattinson. Sanders is married and has two children.
"I'm deeply sorry for the hurt and embarrassment I've caused to those close to me and everyone this has affected," Stewart 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 said he is "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."
Us Weekly published photographic evidence of the affair in its latest issue, with the two in steamy and compromising embraces.
Stewart and Pattinson play lovers in the "Twilight" series, which is set to conclude in November with the release of "The Twilight Saga: Breaking Dawn - Part 2." "Snow White and the Huntsman" was released last month.
Representatives for Stewart, Sanders and Pattinson did not immediately respond to requests for comment.