As we previously reported, American magazine US Weekly had published pictures of K-Stew kissing filmmaker Sanders in Los Angeles, with a source telling the publication that the pair were "all over" each other and "would only take a break [from kissing] when they thought someone was walking by".
The source went on: "It seemed like they couldn't get enough. Kristen was sitting up with her back against the driver's-side window, and this guy was kissing her entire body."
Stewart 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."
41-year old Sanders has since released his own statement, telling Reuters: "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."
While R-Pattz is remaining silent, Rupert's wife Liberty Ross seemed to address his infidelity on Twitter, writing: "If you find it in your heart to care for somebody else, you will have succeeded," before deleting her account.
E! Online has since reported that Kristen's affair with Sanders did NOT start on the set of Snow White And The Huntsman, but on the promotional tour for the flick.
A source told the website: "I can guarantee you 100 percent that nothing happened when they were working--nothing!"
They added that Stewart is planning to 'lay low' for the moment, stating: "She knows she messed up big time. There's no getting around that. She's not doing well, but what do you expect?"
Meanwhile, Lady GaGa has expressed her concern for K-Stew and Rob on Twitter, posting via her official account: "Geez this kirstew rob stuff is brutal. Makes me sad the way press acts. Hope they're ok (sic)."