Jeremy Hunt said he believes he can cause an upset by defeating Boris Johnson in the battle for Number 10 after narrowly securing his place in the final stage of the contest.
The Foreign Secretary beat Michael Gove by just two votes to secure his place on the ballot paper alongside clear favourite Mr Johnson.
Mr Hunt admitted he was the underdog “but in politics surprises happen as they did today”.
“We are going to give Boris the fight of his life,” Mr Hunt said.
“He needs to be ready for that because we’re going to be going out there and making strong arguments that this is the best way to deliver Brexit, with someone who can go and get a better deal from the European Union.”
Former foreign secretary Mr Johnson secured support from more than half the Tory party in the Commons with 160 votes, while Mr Hunt had 77 votes and Mr Gove 75.
The result in the fifth and final ballot came after Mr Gove had managed to finish second in the fourth round, sending shockwaves through the contest.
Allies of Mr Hunt urged MPs not to risk the “personal psychodrama” of a run-off involving the Environment Secretary and his rival Mr Johnson.
Mr Gove’s decision to stand for the leadership in 2016 scuppered Mr Johnson’s campaign and the wounds have not healed.
There was also widespread speculation – denied by Mr Johnson – that supporters of the frontrunner were being encouraged to vote tactically in order to prevent Mr Gove reaching the final ballot.
Following the elimination of Sajid Javid from the race on Thursday morning with 34 votes, at least five of the Home Secretary’s supporters – Chris Philp, Chris Skidmore, Mims Davies, Kevin Foster and Mike Wood – said they would switch to Mr Johnson.
The former foreign secretary’s vote tally only increased by three, raising eyebrows at Westminster.
Sir Alan Duncan, one of Mr Hunt’s supporters, told Channel 4 News: “There’s talk of one team using proxies designed for their candidate being used for another to boost them.
“Well, y’know, this happens in all leadership contests.”
And Simon Clarke, a supporter of Mr Johnson, suggested some MPs may have “freelanced” outside the official campaign.
“I think some people might have taken it upon themselves to try and steer the outcome, ” he said.
But Mr Gove’s campaign manager Mel Stride played down the prospect of a co-ordinated vote-switching operation due to the narrow margin of the defeat.
“It doesn’t seem to me on first observation of this that there has been.
“Because we didn’t see a situation where, as some had speculated, a very large number of votes might have transferred from say Boris Johnson to Jeremy Hunt.
“It would appear to me everybody has behaved pretty much as one would hope they would.”
Mr Johnson said he was “deeply honoured” by the result and “I look forward to getting out across the UK and to set out my plan to deliver Brexit, unite our country, and create a brighter future for all of us”.
Mr Gove said he was “naturally disappointed but so proud of the campaign we ran” and “it’s been an honour to be able to set out a vision for the future of our great country”.
The final outcome of the leadership contest will not be known until the week beginning July 22, with the two remaining candidates taking part in a series of hustings in front of Tory members around the country before the votes are counted.
Mr Johnson and Mr Hunt will also take part in a head-to-head debate on ITV on July 9.
Labour campaign chief Andrew Gwynne said the country faced a choice between “the man who broke the NHS or the man who wants to sell it to Donald Trump” and called for a general election.
“A handful of unrepresentative Conservative members should not be choosing our next prime minister,” he said.