Tory frontrunner Ben Wallace has ruled himself out fo the race to replace Boris Johnson as party leader and Prime Minister.
The defence secretary had been tipped to lead the pack if he threw his hat into the ring.
But in a statement on Twitter, he said: "After careful consideration and discussing with colleagues and family, I have taken the decision not to enter the contest for leadership of the Conservative Party.
"I am very grateful to all my parliamentary colleagues and wider members who have pledged support.
"It has not been an easy choice to make, but my focus is on my current job and keeping this great country safe.
"I wish the very best of luck to all candidates and hope we swiftly return to focusing on the issues that we are all elected to address."
His departure from the running leaves Rishi Sunak, whose resignation hastened Johnson's departure, in pole position.
Mr Sunak announced his leadership bid on Friday with a campaign video in which he promised to confront the difficult economic backdrop with "honesty, seriousness and determination", rather than piling the burden on future generations.
"Someone has to grip this moment and make the right decisions," he said.
Former equalities minister Kemi Badenoch is the latest to throw her hat into the ring, with a plan for a smaller state and a government "focused on the essentials".
The MP for Saffron Walden said she supported lower taxes "to boost growth and productivity, and accompanied by tight spending discipline".
Writing in The Times, she also hit out at "identity politics" and said Boris Johnson was "a symptom of the problems we face, not the cause of them".
MP for North East Derbyshire, Lee Rowley, said he was backing Ms Badenoch.
Meanwhile, former minister Steve Baker has backed Attorney General Suella Braverman's campaign - despite previously saying he was seriously considering putting himself forward for the top job.
Ms Braverman, writing in the Daily Express, promised "rapid and large tax cuts" to ease inflation and said the energy crisis meant "we must suspend the all-consuming desire to achieve net zero by 2050".
Foreign Secretary Liz Truss is also widely expected to run for leader.
Tory MPs Chloe Smith, Julian Knight and Jackie-Doyle Price expressed their support for the senior Cabinet minister on Friday, although she is yet to launch a bid.
Ms Smith said Ms Truss is "the right person to take our country forward", while Mr Knight said she would "deliver on the promise we made to our voters".
Jackie Doyle-Price told The Times Ms Truss would be "a vigorous defender of women's rights" in an apparent reference to her defence of single-sex spaces.
Isle of Wight MP Bob Seely also told BBC Newsnight he believes Ms Truss is most likely to provide "clarity of leadership", and he suspects she will announce her candidacy over the weekend or early next week - although that is "up to her".
Mr Baker, a prominent Brexiteer, had told the PA news agency that Tory blog ConservativeHome "consistently put me in their top 10 for next prime minister, they sometimes put me in their top five".
But he said it would be "very difficult" to persuade colleagues to back him for the party-wide ballot without Cabinet experience.
On Friday evening, he tweeted: "I considered standing for the leadership. My priorities were delivering against our manifesto with our mandate, cutting taxes and seeing through Brexit.
"Happily I no longer need to stand. Suella Braverman will deliver these priorities and more."
Among those publicly backing Mr Sunak are Commons Leader Mark Spencer, former Tory Party co-chairman Oliver Dowden, former chief whip Mark Harper, ex-ministers Liam Fox and Andrew Murrison, and MPs Sir Bob Neill and Paul Maynard.
The former chancellor released a glossy launch video in which he set out his family history, saying: "Our country faces huge challenges, the most serious for a generation.
"And the decisions we make today will decide whether the next generation of British people will also have the chance of a better future."
Those in support of Mr Sunak have been sharing a link to his campaign website, http://www.ready4rishi.com.
It appears that a site with a slightly different name, http://www.readyforrishi.com, which redirects to the official campaign page, was set up in December 2021.
Mr Sunak's team said domains are bought all the time, adding that they had been transferred a number of them.
Even before he made his formal announcement, Mr Sunak had come under fire from Johnson loyalists, with Brexit opportunities minister Jacob Rees-Mogg denouncing him as a "high tax chancellor" who failed to curb inflation.
Mr Rees-Mogg went on to tell the BBC's Any Questions on Friday: "I will not be endorsing Mr Sunak for prime minister.
"I belong to a party that believes in low taxation and the former chancellor has talked about low taxation and delivered higher taxation."
The absence of a clear front-runner in the leadership race has tempted a number of less-fancied contenders to step forward - with backbencher John Baron saying he will be "taking soundings" over the weekend.
Tom Tugendhat, the chairman of the Commons Foreign Affairs Committee, has already said he will be be putting his name forward.
More are expected in the coming days including Mr Sunak's successor as chancellor, Nadhim Zahawi, and Ms Truss.
While Mr Zahawi has not yet launched a bid, Tory peer and minister Lord Goldsmith said on Friday evening he "stands apart from most rivals".
Elsewhere, Defence Secretary Ben Wallace is tipped to be a front-runner should he mount his own campaign.
Defence minister James Heappey told The Telegraph in comments reported on Friday that Mr Wallace had "spent the last 48 hours thinking really hard about whether he wants to do it".
"He says it straight," he said. "There is a dimension that Ben is now known on the world stage as a safe pair of hands.
"His biggest selling point is that he is good, honest, decent, hard working, communicates in a way the public understands and likes and is honest about what he does and doesn't know."
Following elections to the executive of the backbench 1922 Committee on Monday, the new body will draw up a timetable for the leadership election.
