Embarrassing, racially tinged emails about President Barack Obama’s imagined movie tastes, posted online by hackers, prompted public apologies Thursday from Sony Pictures Entertainment’s movie chief and one of its top producers.

“To anybody I’ve offended, I’m profoundly and deeply sorry, and I regret and apologize for any injury they might have caused,” film producer Scott Rudin said in a statement after the disclosure of his private email banter with Amy Pascal, Sony’s co-chairwoman, about Obama and black-themed films.

Pascal said in her own statement: “Although this was a private communication that was stolen, I accept full responsibility for what I wrote and apologize to everyone who was offended.”

The email exchange in question, reported by BuzzFeed, took place before Pascal attended a breakfast for Obama that was organized by Jeffrey Katzenberg, the chief executive of DreamWorks Animation.

“What should I ask the president at this stupid Jeffrey breakfast?” Pascal asked Rudin in an opening query. She then speculated that she might ask if Obama liked “Django Unchained,” about a former slave. Rudin countered with a suggestion about “12 Years a Slave.”

People familiar with Sony’s response to the attack, who spoke on the condition of anonymity because they were not authorized to comment, have said they expected to face further unauthorized disclosures in the days ahead.