The Hollywood actor Tilda Swinton has published the full text of an email exchange she shared with the American comedian Margaret Cho, after the comic said Swinton had treated her “like her house servant” during a discussion about diversity in the Marvel film Doctor Strange.

Swinton released the email conversation to a US website after Cho told a US podcast that she and Swinton had had a “fight” over the fact that the British actor had been cast in the movie as the Ancient One, a character who was Asian in the original comic book series.

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Cho, a stand-up comic whose work frequently focuses on race and gender issues, told TigerBelly last week that Swinton had contacted her to say “she didn’t understand why people were so mad about Doctor Strange and she wanted to talk about it, and wanted to get my take on why all the Asian people were mad”.

Margaret Cho on stage. Photograph: PR

“[She] was like, ‘Could you please tell them … ’” Cho told the podcast. “I’m like, ‘Bitch, I can’t tell them … I don’t have a yellow phone under a cake dome.’”

But after an account of the podcast was published by the website Jezebel, Swinton’s representative forwarded what he called “the entire unedited and only conversation she has ever had with Margaret – with her gratitude for the opportunity to clarify”.

While Cho had characterised their conversation as a “fight”, the tone of the emails, on the surface at least, is more cordial. Swinton first contacted Cho on 13 May this year, saying that while they had never met, “I’m a fan”, and she wanted to ask a favour.

“The diversity debate – ALL STRENGTH to it – has come knocking at the door of Marvel’s new movie DR STRANGE,” Swinton wrote, but said she was unaware of the debate since she didn’t use social media. “I would really love to hear your thoughts and have a – private – conversation about it.”

In response, Cho declared herself in turn “a big fan of yours”, then wrote: “The character you played in Dr Strange was originally written as a Tibetan man and so there’s a frustrated population of Asian Americans who feel the role should have gone to a person of Asian descent.”

The broader debate, Cho wrote, was to do with the “whitewashing” of Asians in American films. “Our stories are told by white actors over and over again and we feel at a loss to know how to cope with it.”

Marvel has repeatedly been forced to defend Swinton’s casting, with the film’s screenwriter hinting the character’s race was changed from Tibetan to avoid upsetting China.

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Similar accusations have been made by Asian-American actors about a range of films including Ghost in the Shell, in which Scarlett Johansson was cast as the manga character Major Motoko Kusanagi, renamed Major for the movie, and Aloha, in which the part of a quarter-Chinese, quarter-native Hawaiian called Allison Ng was played by the blonde, blue-eyed Emma Stone.

In her response to Cho, Swinton wrote that Marvel had made “a conscious effort to shake up stereotypes” by casting Chiwetel Ejiofor in a role that was originally white, and that she had personally been cheered by the fact the “wise old Eastern Geezer Fu Manchu” part had been offered to her as a woman in her 50s.

“Diversity is pretty much my comfort zone,” she wrote. “The idea of being caught on the wrong side of this debate is a bit of a nightmare to me.”

Cho responded by saying that she accepted that as an artist Swinton was “about diversity”, “but this particular case of the Ancient One is just another in a long list of ‘whitewashed’ Asian characters, and so you’re likely to feel the heat of history.” She suggested that Swinton could help by producing more films with roles for Asian-Americans, to which the actor replied that she was currently developing a part Korean-language film with a number of Korean leads.

Contacted for a response after Swinton published her emails, Cho released a statement saying: “Asian actors should play Asian roles. I believe my emails stand on their own and should be taken for the spirit in which they were intended.” She remained a “huge fan” of Swinton, she said.