Elon Musk has defended his stance on diversity and free speech in a tense interview with the former CNN anchor Don Lemon.

The Tesla chief executive was openly irritated by Lemon’s line of questioning during the hour-long video interview, published on Monday.

Responding to a question about his prescription for ketamine, Musk said: “It’s pretty private to ask somebody about a medical prescription.” He said he took the drug to address “a negative chemical state in my in my brain, like depression”.

Asked if he abused the drug, which is commonly used as an anaesthetic, he said: “I don’t think so. If you use too much ketamine you can’t really get work done. I have a lot of work.”

Musk, who cancelled a deal between his X platform and Lemon after the interview was taped earlier this month, was asked about his criticism of diversity, equity and inclusion (DEI) schemes including his support for a thread on X by Ben Shapiro, a conservative pundit, claiming that DEI was endangering medical patients.

Lemon told Musk there was “no evidence” that DEI schemes were lowering the standards for medical practice, prompting the billionaire to say the response to the interview by X users would help them “make their own decision” on the issue.

Asked if he believed in DEI, Musk said: “I think we should … treat people according to their skills and integrity.”

Musk also defended X’s content moderation standards after Lemon highlighted antisemitic and racist posts that were still on the platform, which the Tesla CEO bought in 2022.

Asked why they had not been deleted, Musk indicated the posts were not illegal and said: “So, Don, you love censorship, is what you’re saying.” Lemon replied that he believed in moderation, to which Musk replied: “Moderation is a propaganda word for censorship.”

If a post was illegal, “we’re going to take it down”, said Musk, adding that if it did not break the law, “we’re putting our thumb on the scale or being censors”.

Musk made clear his irritation with Lemon at several points. The host asked him if he was upset and the entrepreneur responded that “you are upsetting me because the way you’re phrasing questions … is not cogent”.

Musk told Lemon the next Tesla Roadster model would be a collaboration with his SpaceX business and “would have some rocket technology in it”.

He added: “I think the only way to do something that’s cooler than the Cybertruck is to combine SpaceX and Tesla technology to create something that’s not even really a car.” Asked if it was a flying car, Musk said: “Maybe.”

Musk also confirmed he had recently met Donald Trump, but said he had not donated to his campaign, although he was “leaning away” from supporting Joe Biden. Asked if he was going to back a presidential runner, he said: “I may in the final stretch endorse a candidate, but I don’t know yet.”