Kemi Badenoch has said Tory rebels plotting to remove Rishi Sunak with the aim of installing her as leader are not her "friends" and should "stop messing around".
The business secretary, who ran for the Tory leadership following the demise of Boris Johnson, insisted she did not want to oust the prime minister and urged the party to unite behind him.
Speaking to Sunday Morning with Trevor Phillips, the minister - who is emerging as a key figure on the Tory right - accused some MPs disillusioned with Mr Sunak's leadership of "stirring" and "creating problems" for the party.
Politics latest: Post Office 'problems' go beyond Horizon scandal
"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," she said.
"I fully support the prime minister and I have said many times that I stood to be leader and lost, and the last time we had a contest after Liz Truss resigned I said that the right person to lead the country was Rishi Sunak, and I still believe that to be the case."
Speculation about a further potential leadership election has been building after Sir Simon Clare, the former levelling up secretary under Ms Truss, called on Mr Sunak to resign as prime minister, arguing it was the only way for the Conservatives to avoid a "massacre" at the next election.
Although Sir Simon insisted he was acting alone, it later emerged that a handful of ex-advisers and MPs were meeting to discuss a potential change in leader - the third in this parliament.
Will Dry, a former adviser to Mr Sunak who left his role last year, is thought to have joined "others" who believe the Tories "are heading for the most almighty of defeats" at the general election and that the Conservative Party "won't exist by Christmas" if Nigel Farage makes another political comeback.
Speaking to Sky News, Nadine Dorries, the former culture secretary and ally of Mr Johnson, claimed there were people in the Conservative Party who saw Ms Badenoch as "their project".
"What she should be doing, what they all should be doing, is getting behind Rishi Sunak because it's insanity to think we can have another leadership election."
Ms Badenoch, who consistently tops popularity polls with Tory members, firmly rejected suggestions there should be a change in leader.
"This is not a popularity contest," she told Sir Trevor. "This is about running the country."
She said Tory MPs "can't just keep treating prime ministers as if they are disposable - 'Oh, the polls aren't doing so well, so let's toss someone else and find another person'", adding: "That is quite wrong."
Pressed on rumours that she was seen as the ideal replacement for those who want to remove Mr Sunak, Ms Badenoch replied: "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. They don't care about me. They don't care about my family or what this would entail. They are just stirring.
"We have 350 MPs, this is a small number of people who are doing this. The vast majority of Conservative MPs support the prime minister."