Her name is at the centre of intense speculation over who could replace him, but she insisted the shadowy group were not her friends.
“They don’t care about me. They don’t care about my family or what this would entail. They are just stirring,” she said.
But she did not rule out a future tilt at the top job, saying “You never know these things [standing again] until you’re in the moment”.
The beleaguered Mr Sunak is the focus of a plot by MPs, donors and former aides to force him from office.
Ms Badenoch’s name has been put forward as the possible “consensus” candidate to replace him – the MP who could command the most support across the party.
Asked about the plot on Sky’s Sunday Morning with Trevor Phillips, she said: “A lot of people who are going around doing this are creating problems and difficulties that the party and, more importantly, the country does not need.
“I fully support the prime minister.”
Those putting her name forward are not her friends, she said, adding: “They need to stop messing around and get behind the leader.
“The fact of the matter is most people in the country are not interested in all of this Westminster tittle-tattle. Quite frankly, the people who keep putting my name in there are not my friends.”
Tory donors recently funded an explosive poll that predicted a devastating Labour landslide unless Mr Sunak was removed as leader.
Tory peer Lord Frost, who organised the poll, has been warned he risks losing the party whip unless he comes clean and names the anonymous moneymen.
And this week a senior Tory linked to Liz Truss and Boris Johnson, Sir Simon Clarke, went public with calls for his party leader to go.
Ms Badenoch said she called Sir Simon afterwards “and asked him what on earth he was doing”.
She warned the Tory party cannot keep treating prime ministers as “disposable”, as she said she was “extremely” frustrated at the speculation.
But another Boris Johnson ally, Nadine Dorries accused Ms Badenoch of pursuing her leadership ambitions despite the denials.
On Ms Badenoch’s effective call for the plotters to shut up, Ms Dorries said: “She should take her own advice.”
She also accused the business secretary and former immigration minister, Robert Jenrick, seen as another leadership contender, of self-interest, saying: “What they are out for is themselves.”
Tim Montgomerie, who worked for Boris Johnson in Downing Street, said Tory members watching her interview would be thinking: “I would not mind Kemi as leader.”
A secret group of up to seven former advisers have been accused of running the campaign, dubbed the “Sheekey plotters” after a well-known seafood restaurant, J Sheekey, in central London they are said to frequent.
One was publicly unveiled as Will Dry, a former No 10 special adviser who worked on polling, while others are reported to have threatened to sue those who publicly name them.
The group are thought to be planning a war of attrition against the prime minister and are seen as upcoming “pain points” for the Tory leader, including looming by-elections and the local elections in May.
No 10 has taken to calling their attacks the “grid of s***”, a play on the Downing Street “grid” which dictates when government announcements will be made.