May said the debate should focus on the UK's future rather than her own political career.
Theresa May on Sunday revealed her irritation at the constant speculation over her future as British prime minister as her Conservative party MPs continue to be divided over the direction the Brexit negotiations should take.
In a BBC interview to mark the six-month to the March 2019 deadline for Britain's formal exit from the European Union (EU), May said the debate should focus on the UK's future rather than her own political career.
"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," she said.
"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," said the British PM, who remains at the heart of a Tory party split over her leadership.
Her comments come days after her party MPs opposed to her Brexit plan met to discuss how and when they could force her to stand down. Around 50 Brexiteer members of the European Research Group (ERG) met on Tuesday to discuss a leadership challenge.
May also criticised former foreign secretary Boris Johnson, seen as a frontrunner in any leadership challenge as the most prominent Brexiteer within the party, for his recent attacks on government strategy in his newspaper columns.
The British PM said his language was "completely inappropriate" when he described her Brexit strategy as putting the UK in a "suicide vest" and handing the detonator to Brussels.
"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," she said.
May's leadership of the Conservative party has been precarious since the resignation of Johnson from the Cabinet over her Brexit blueprint in July and has been seen as fragile ever since her 2017 snap general election gamble when the party lost its majority in Parliament.
As part of her so-called Chequers plan for Britain's future relationship with the EU, May said she wants to strike a trade deal with the EU for after the UK leaves in 2019. She also said there needs to be "friction-free movement of goods" with no customs or regulatory checks between the UK and EU on the island of Ireland, in order to avoid a hard border there.
The UK and EU are hoping to agree a way forward next month, at the same time as they settle the terms of the UK's withdrawal, including a transition period up to the end of 2020.
The British PM stressed that she remained a "bloody difficult woman" a description which was used to describe her by former Conservative party Chancellor Ken Clarke.
"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," she said.
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