The Prime Minister insisted she was focused on the country’s future rather than her own, in a BBC interview to mark the six-month countdown to Brexit.
Mrs May criticised Mr Johnson for using “completely inappropriate” language when he described her Brexit strategy as putting the UK in a “suicide vest”.
Around 50 Brexiteers met to war-game ways to oust the Prime Minister on Tuesday evening and Mr Johnson is widely-expected to vie to replace Mrs May.
Asked if she would reassure the Conservative party she was not determined to go on and on, the PM told BBC Panorama’s Inside No 10: Deal or No Deal?: “I get a little bit irritated but this debate is not about my future, this debate is about the future of the people of the UK and the future of the United Kingdom.
“That’s what I’m focused on and that’s what we should all be focused on.
“It’s ensuring that we get that good deal from the European Union which is good for people in the UK, wherever they live in the UK, that’s what’s important for us ... It’s the future of people in the UK that matters.”
Mr Johnson faced a Tory backlash after comparing Mrs May’s Brexit plan to a “suicide vest” and his former communications director, Guto Harri, said on Saturday that his ex-boss was “digging his political grave”.
Mrs May said the former foreign secretary’s comments were “not right”.
“I have to say that that choice of language is completely inappropriate,” she said.
“I was home secretary for six years, and as Prime Minister for two years now I think using language like that was not right and it’s not language I would have used.”
The PM was once described as “bloody difficult woman” by former Cabinet minister Ken Clarke, and later claimed the description as a badge of honour.
She told the programme that person is “still there”, but “there’s a difference between those who think you can only be bloody difficult in public, and those who think actually you bide your time, and you’re bloody difficult when the time is right - and when it really matters.”