“The only reason you mock something is when it doesn’t live up to the ideal,” he said. “There’s a huge difference between what these journalists are doing on the ground, and the perversion of it that is the 24-hour news networks.”

Bringing “Rosewater” to the screen, Mr. Stewart said, was not about acquainting viewers with who he is as a director, but getting himself comfortable with a storytelling medium in which the story does not emanate solely from him. “I’ve never been part of an audience for something I’ve done,” he said. “I’ve always been the performer. They’re always looking at me. It’s been the greatest thing, to be able to see something you’ve done, while snacking. I can have Raisinets and watch.”

Mr. Stewart, who lost Mr. Oliver to HBO after his “Daily Show” hiatus, was less sanguine about whether Comedy Central would give him time off in the future to make another movie. “I had a hard enough time, getting them to let me have this one,” he said.

The process of creating and promoting “Rosewater” has deepened the friendship between Mr. Stewart and Mr. Bahari, who check in on each other’s families, tease each other and share startlingly similar cultural references. This movie “is hardly ‘Not Without My Daughter, Part II,' ” Mr. Bahari said, nodding to that 1991 Sally Field melodrama. Mr. Stewart joked, “Well, that is actually my next project.”

Even when Mr. Bahari, who once considered himself an intensely private person, acknowledged that “Rosewater” had taught him the value of opening up about his imprisonment and sharing his story, he could not help doing so in a familiar acerbic tone.

“I’ve watched Oprah, so I know how much it helps to talk about this,” he said. “Jon was my own personal Dr. Phil.”

As if beaming with pride for his quip-firing disciple, Mr. Stewart, the sarcastic master, said: “I’m his life coach now. There have been a lot of trust exercises. I can’t tell you how many times he’s fallen backwards off a table, into my arms.”