The comments were made in a series of leaked email exchanges between Mr. Rudin and Sony Pictures Entertainment co-chairman Amy Pascal, who also apologized Thursday. It was yet another embarrassment in the ongoing Sony hacking scandal, in which highly sensitive material is being leaked almost daily.
"Private emails between friends and colleagues written in haste and without much thought or sensitivity, even when the content of them is meant to be in jest, can result in offense where none was intended," Rudin said in a statement to industry site Deadline after the Obama remarks surfaced.
"I made a series of remarks that were meant only to be funny, but in the cold light of day, they are in fact thoughtless and insensitive — and not funny at all. To anybody I've offended, I'm profoundly and deeply sorry, and I regret and apologize for any injury they might have caused."
In a statement released soon after by Sony, Ms. Pascal called her comments "insensitive and inappropriate" and "not an accurate reflection of who I am." She said that although the emails were "stolen," she accepts "full responsibility for what I wrote and apologize to everyone who was offended."
In a tweet later Thursday, "Scandal" and "Grey's Anatomy" creator Shonda Rhimes said the comments were "racist," not merely "racially insensitive."
This latest shocker in the Sony scandal erupted Tuesday, when the website Gawker posted email exchanges stolen from the studio's computer systems. The leaks gave the public a rare, unfiltered glimpse into the blunt, often crude way Hollywood does business.
The emails drawing most of the attention this week were primarily between Rudin, producer of the Academy Award-winning "No Country for Old Men," and Pascal, who has held the position since 2006. The two have a decades-old friendship, thanks, in part, to a longstanding deal with the studio, where they've worked jointly on projects like "The Social Network."
When juxtaposed with the saccharine graciousness of Hollywood's awards season, the emails reveal a much darker and, to some, surprising side of the industry.
"She's a camp event and a celebrity and that's all," wrote Rudin of Jolie in one exchange about a potential "Cleopatra" project.
In another, as reported by Buzzfeed, Rudin and Pascal also riffed about what she should talk to President Obama about at an upcoming fundraiser.
"Should I ask him if he liked DJANGO?" Pascal asked, referring to Quentin Tarantino's "Django Unchained."
They continued the email chain joking about which films the President might enjoy, referencing "Lee Daniels' The Butler," ''Think Like a Man" and "Ride Along" — all films with primarily African American casts.
"I bet he likes Kevin Hart," wrote Rudin.
In a separate email exchange obtained by Gawker, Sony CEO Michael Lyton also called Hart a "whore" for asking to get compensated for promotional tweets.
"I look at myself as a brand and because of that, I will never allow myself to be (taken) advantage of," Hart responded on Instagram.
Rev. Al Sharpton said in a statement that the apologies were not enough, comparing Pascal to disgraced NBA owner Donald Sterling and demanding that she meet with black leaders immediately.
Beyond the scintillating behind-the-scenes peek at the film business, Hollywood is somewhat divided on how to feel to about the unflattering exposure and what it means for Sony. Many are concerned about the ethics of diving into the leaked assets, which have included films, executive salaries, and the Social Security numbers of nearly everyone who has received a paycheck from Sony.
"You can't hold people responsible on how they conduct (emailing) in private or between colleagues, unless they're doing something illegal," comedian Ricky Gervais told the AP.
"It almost seems like it's a story line from a film," said "Foxcatcher" star Steve Carell. "But the truth is stranger than fiction, I guess."
Representatives for Jolie did not immediately respond to the AP's request for comment, nor did the White House communications office.
AP Entertainment Writers Sandy Cohen and Derrik Lang contributed to this report.