The eye-catching photo of the Prime Minister and Trump - which flashed around the world and dominated British newspaper front pages - was his attempt to steady her on her feet as they walked down a ramp, May told the style magazine American Vogue.
The awkward moment, followed by the President patting May's hand in his, sparked suggestions that he was overstepping usual etiquette in being so tactile. But May said:
"I think he was actually being a gentleman. We were about to walk down a ramp, and he said it might be a bit awkward."
Some on social media were not willing to give the President the benefit of the doubt.
Many reminded Trump of his track record of sexism and misogyny when he tweeted a message of support for International Women's Day - and it was more than his hot mic comments on the infamous 2005 bus ride with former "Access Hollywood" host Billy Bush.
In the wide-ranging interview, the Prime Minister appeared in a series of photographs by Annie Leibovitz and answered questions on issues including the constant comparison between her Margaret Thatcher.
"There can only ever be one Margaret Thatcher," she says. "I'm Theresa May. I do things my way."
She was also asked if she had a superpower, what would it be:
"I think I'd want to make sure that everyone in the world had access to clean water and sufficient food, so that we didn't see people starving."
This went down particularly badly with some:
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