Rylance plays a larger-than-life outcast in Disney's "The BFG," directed by Steven Spielberg.
The 56-year-old Brit has been a theater actor for years. He snagged a best supporting actor Oscar for his first Hollywood role, playing Rudolf Abel in "Bridge of Spies" — another Spielberg film.
"It means the world to me that the stories I'm telling are making people laugh or moving people or just ... distracting themselves from the troubles of the world for a day and giving them a bit of strength to carry on," Rylance said in an interview with ABC News' Abbie Boudreau.
"The BFG" — a tale of two unlikely friends — hits those marks, with themes like finding the strength to overcome differences.
Rylance said the film tells the story of "a very loving friendship."
The movie even includes a special language, which Rylance demonstrated for Boudreau.
"The BFG" premieres July 1.
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