Abrams will also be directing Disney's next "Star Wars" film in 2015, and Stewart is a fan of both.
The conversation quickly took a turn with Abrams addressing the differences between the two — apparently he sees "Star Wars" as a "samurai""Western"— and his initial dislike of "Star Trek" for the longest time.
Abrams also discussed how he improved upon the original "Star Trek" series with his films, unintentionally bashing the popular television show in the process.
"The original show was kind of static," said Abrams. "They couldn't afford to go anywhere or do anything. And we had a slightly larger budget than they did."
"Star Trek Into Darkness" is out in theaters Thursday.
Watch an extended cut of their interview below: