"What should I ask the president at this stupid Jeffrey breakfast?" Pascal wrote to Rudin, referring to a breakfast hosted by DreamWorks' Jeffrey Katzenberg.
"Would he like to finance some movies," Rudin responds, to which Pascal replies, "I doubt it. Should I ask him if he liked DJANGO?"
Their comments have sparked outrage among some Hollywood figures, including Shonda Rhimes, who took issue with media outlets referring to the messages as merely "racially insensitive."
Rev. Al Sharpton also slammed the emails as "offensive" and "insulting," according to the New York Times. And Lisa Kudrow told The Huffington Post, "Don't write anything you don't want broadcast in an email. ... Everything is broadcast and published."
This is the latest in a series of embarrassing incidents for Rudin and Pascal in the wake of the Sony hacking. Other leaked emails between them refer to Angelina Jolie as a "minimally talented spoiled brat."
Rudin and Pascal have both since apologized for their remarks about President Obama.
"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 told Deadline. "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."
Added Pascal, in a statement to Variety: "The content of my emails were insensitive and inappropriate but are not an accurate reflection of who I am. Although this was a private communication that was stolen, I accept full responsibility for what I wrote and apologize to everyone who was offended."
What do you think of Pascal and Rudin's comments?